diff --git a/muxplex/frontend/app.js b/muxplex/frontend/app.js
index 302b419..ea3bb55 100644
--- a/muxplex/frontend/app.js
+++ b/muxplex/frontend/app.js
@@ -862,6 +862,10 @@ async function openSession(name, opts = {}) {
     updateSessionPill(_currentSessions);
   }
 
+  // Hide FAB during fullscreen session view
+  const fab = $('new-session-fab');
+  if (fab) fab.classList.add('hidden');
+
   // Connect to session (kill old ttyd, spawn new one for this session)
   try {
     if (!opts.skipConnect) {
@@ -903,6 +907,10 @@ function closeSession() {
   const pill = $('session-pill');
   if (pill) pill.classList.add('hidden');
 
+  // Restore FAB when returning to overview
+  const fab = $('new-session-fab');
+  if (fab) fab.classList.remove('hidden');
+
   return Promise.resolve();
 }
 
@@ -1348,6 +1356,8 @@ function bindStaticEventListeners() {
   if (newSessionBtn) on(newSessionBtn, 'click', function() { showNewSessionInput(newSessionBtn); });
   var sidebarNewSessionBtn = $('sidebar-new-session-btn');
   if (sidebarNewSessionBtn) on(sidebarNewSessionBtn, 'click', function() { showNewSessionInput(sidebarNewSessionBtn); });
+  var newSessionFab = $('new-session-fab');
+  if (newSessionFab) on(newSessionFab, 'click', function() { showNewSessionInput(newSessionFab); });
   on($('sidebar-toggle-btn'), 'click', toggleSidebar);
   on($('sidebar-collapse-btn'), 'click', toggleSidebar);
   bindSidebarClickAway();
diff --git a/muxplex/frontend/index.html b/muxplex/frontend/index.html
index f5cf808..55ec634 100644
--- a/muxplex/frontend/index.html
+++ b/muxplex/frontend/index.html
@@ -69,6 +69,9 @@
     <span id="session-pill-bell" class="session-pill__bell hidden" aria-hidden="true">&#128276;</span>
   </button>
 
+  <!-- ── Mobile FAB (new session) ───────────────────────────────────────────── -->
+  <button id="new-session-fab" class="new-session-fab" aria-label="New session">+</button>
+
   <!-- ── Toast notification ─────────────────────────────────────────────────── -->
   <div id="toast" class="toast hidden" role="status" aria-live="polite" aria-atomic="true"></div>
 
diff --git a/muxplex/frontend/style.css b/muxplex/frontend/style.css
index 99ec2cc..1ad9f3f 100644
--- a/muxplex/frontend/style.css
+++ b/muxplex/frontend/style.css
@@ -1201,6 +1201,34 @@ body {
   border-color: var(--text-muted);
 }
 
+/* ============================================================
+   Mobile FAB — new session floating action button
+   ============================================================ */
+
+.new-session-fab {
+  display: none;
+  position: fixed;
+  bottom: 16px;
+  right: 16px;
+  width: 56px;
+  height: 56px;
+  border-radius: 50%;
+  background: var(--accent);
+  color: var(--bg);
+  border: none;
+  font-size: 28px;
+  font-weight: 300;
+  line-height: 1;
+  cursor: pointer;
+  z-index: 100;
+  box-shadow: 0 4px 12px rgba(0, 0, 0, 0.4);
+  transition: transform 150ms ease, box-shadow 150ms ease;
+}
+
+.new-session-fab:active {
+  transform: scale(0.95);
+}
+
 /* ============================================================
    Responsive overlay sidebar at <960px
    ============================================================ */
@@ -1228,4 +1256,15 @@ body {
   .sidebar-collapse-btn {
     display: none;
   }
+
+  /* Mobile FAB: show on mobile, hide header + button */
+  .new-session-fab {
+    display: flex;
+    align-items: center;
+    justify-content: center;
+  }
+
+  #new-session-btn {
+    display: none;
+  }
 }
diff --git a/muxplex/tests/test_frontend_css.py b/muxplex/tests/test_frontend_css.py
index 96984ca..4048836 100644
--- a/muxplex/tests/test_frontend_css.py
+++ b/muxplex/tests/test_frontend_css.py
@@ -1488,3 +1488,121 @@ def test_css_sidebar_new_btn_hover_exists() -> None:
     assert ".sidebar-new-btn:hover" in css, (
         "Missing .sidebar-new-btn:hover rule in style.css"
     )
+
+
+# ============================================================
+# Mobile FAB (task-6-mobile-fab)
+# ============================================================
+
+
+def test_css_fab_class_exists() -> None:
+    """.new-session-fab CSS rule must exist."""
+    css = read_css()
+    assert ".new-session-fab" in css, "Missing .new-session-fab rule in style.css"
+
+
+def test_css_fab_display_none_by_default() -> None:
+    """.new-session-fab must have display:none as default (hidden on desktop)."""
+    import re
+    css = read_css()
+    # Find the .new-session-fab block (non-media-query context)
+    # Match the block that is NOT inside a @media rule
+    # Look for .new-session-fab { ... display: none ... } outside of @media
+    # Simple check: the rule body should contain 'display' before the first @media containing it
+    match = re.search(r'\.new-session-fab\s*\{([^}]*)\}', css)
+    assert match, ".new-session-fab rule not found"
+    body = match.group(1)
+    assert "display" in body and ("none" in body or "display:none" in body.replace(" ", "")), (
+        f".new-session-fab must have display:none by default, got body: {body!r}"
+    )
+
+
+def test_css_fab_position_fixed() -> None:
+    """.new-session-fab must be position:fixed."""
+    import re
+    css = read_css()
+    match = re.search(r'\.new-session-fab\s*\{([^}]*)\}', css)
+    assert match, ".new-session-fab rule not found"
+    body = match.group(1)
+    assert "position" in body and "fixed" in body, (
+        f".new-session-fab must have position:fixed, got: {body!r}"
+    )
+
+
+def test_css_fab_size_56px() -> None:
+    """.new-session-fab must be 56px width and height."""
+    import re
+    css = read_css()
+    match = re.search(r'\.new-session-fab\s*\{([^}]*)\}', css)
+    assert match, ".new-session-fab rule not found"
+    body = match.group(1)
+    assert "56px" in body, (
+        f".new-session-fab must have 56px size (width/height), got: {body!r}"
+    )
+
+
+def test_css_fab_border_radius_50_percent() -> None:
+    """.new-session-fab must have border-radius:50% for circular shape."""
+    import re
+    css = read_css()
+    match = re.search(r'\.new-session-fab\s*\{([^}]*)\}', css)
+    assert match, ".new-session-fab rule not found"
+    body = match.group(1)
+    assert "50%" in body, (
+        f".new-session-fab must have border-radius:50%, got: {body!r}"
+    )
+
+
+def test_css_fab_mobile_media_query_shows_flex() -> None:
+    """At max-width: 959px, .new-session-fab must be shown as display:flex."""
+    import re
+    css = read_css()
+    # Find the 959px media query and check that .new-session-fab uses display:flex
+    match = re.search(
+        r'@media\s*\([^)]*max-width\s*:\s*959px[^)]*\)\s*\{([^@]*)\}',
+        css,
+        re.DOTALL
+    )
+    assert match, "Missing @media (max-width: 959px) block"
+    media_body = match.group(1)
+    assert ".new-session-fab" in media_body, (
+        "@media (max-width: 959px) block must contain .new-session-fab rule"
+    )
+    # Find the .new-session-fab rule within the media query
+    fab_match = re.search(r'\.new-session-fab\s*\{([^}]*)\}', media_body)
+    assert fab_match, ".new-session-fab rule not found in 959px media query"
+    fab_body = fab_match.group(1)
+    assert "flex" in fab_body, (
+        f".new-session-fab must show as display:flex in 959px media query, got: {fab_body!r}"
+    )
+
+
+def test_css_fab_mobile_media_query_hides_new_session_btn() -> None:
+    """At max-width: 959px, #new-session-btn must be hidden."""
+    import re
+    css = read_css()
+    match = re.search(
+        r'@media\s*\([^)]*max-width\s*:\s*959px[^)]*\)\s*\{([^@]*)\}',
+        css,
+        re.DOTALL
+    )
+    assert match, "Missing @media (max-width: 959px) block"
+    media_body = match.group(1)
+    assert "#new-session-btn" in media_body, (
+        "@media (max-width: 959px) block must contain #new-session-btn rule to hide it"
+    )
+    # Find the #new-session-btn rule and verify it has display:none
+    btn_match = re.search(r'#new-session-btn\s*\{([^}]*)\}', media_body)
+    assert btn_match, "#new-session-btn rule not found in 959px media query"
+    btn_body = btn_match.group(1)
+    assert "none" in btn_body, (
+        f"#new-session-btn must have display:none in 959px media query, got: {btn_body!r}"
+    )
+
+
+def test_css_fab_active_transform() -> None:
+    """.new-session-fab:active must have a transform rule (scale)."""
+    css = read_css()
+    assert ".new-session-fab:active" in css, (
+        "Missing .new-session-fab:active rule in style.css"
+    )
diff --git a/muxplex/tests/test_frontend_html.py b/muxplex/tests/test_frontend_html.py
index 66917c9..93535bb 100644
--- a/muxplex/tests/test_frontend_html.py
+++ b/muxplex/tests/test_frontend_html.py
@@ -949,3 +949,53 @@ def test_html_sidebar_structure_complete() -> None:
     assert header is not None, "Missing .sidebar-header in #session-sidebar"
     assert list_ is not None, "Missing #sidebar-list in #session-sidebar"
     assert footer is not None, "Missing .sidebar-footer in #session-sidebar"
+
+
+# ============================================================
+# Mobile FAB (task-6-mobile-fab)
+# ============================================================
+
+
+def test_html_fab_exists() -> None:
+    """#new-session-fab button must exist with class new-session-fab, aria-label='New session', text '+'."""
+    soup = _SOUP
+    fab = soup.find(id="new-session-fab")
+    assert fab is not None, "Missing #new-session-fab"
+    assert fab.name == "button", (
+        f"#new-session-fab must be a <button>, got: {fab.name}"
+    )
+    classes = fab.get("class") or []
+    assert "new-session-fab" in classes, (
+        f"#new-session-fab must have class 'new-session-fab', has: {classes}"
+    )
+    assert fab.get("aria-label") == "New session", (
+        f"#new-session-fab must have aria-label='New session', got: {fab.get('aria-label')!r}"
+    )
+    text = fab.get_text(strip=True)
+    assert text == "+", (
+        f"#new-session-fab text must be '+', got: {text!r}"
+    )
+
+
+def test_html_fab_before_toast() -> None:
+    """#new-session-fab must appear before #toast in the document."""
+    soup = _SOUP
+    fab = soup.find(id="new-session-fab")
+    toast = soup.find(id="toast")
+    assert fab is not None, "Missing #new-session-fab"
+    assert toast is not None, "Missing #toast"
+    # Find positions in the flat list of all elements
+    all_elements = list(soup.find_all(True))
+    fab_idx = next(
+        (i for i, el in enumerate(all_elements) if el.get("id") == "new-session-fab"),
+        None,
+    )
+    toast_idx = next(
+        (i for i, el in enumerate(all_elements) if el.get("id") == "toast"),
+        None,
+    )
+    assert fab_idx is not None, "#new-session-fab not found in element list"
+    assert toast_idx is not None, "#toast not found in element list"
+    assert fab_idx < toast_idx, (
+        f"#new-session-fab (idx={fab_idx}) must appear before #toast (idx={toast_idx})"
+    )
diff --git a/muxplex/tests/test_frontend_js.py b/muxplex/tests/test_frontend_js.py
index 5552d41..6b10007 100644
--- a/muxplex/tests/test_frontend_js.py
+++ b/muxplex/tests/test_frontend_js.py
@@ -1798,3 +1798,63 @@ def test_bind_sidebar_new_session_btn_in_bind_static_event_listeners() -> None:
     assert "showNewSessionInput" in body, (
         "bindStaticEventListeners must call showNewSessionInput for the sidebar new-session button"
     )
+
+
+# ============================================================
+# Mobile FAB (task-6-mobile-fab)
+# ============================================================
+
+
+def test_js_fab_bound_in_bind_static_event_listeners() -> None:
+    """bindStaticEventListeners must bind #new-session-fab click to showNewSessionInput."""
+    match = re.search(
+        r"function bindStaticEventListeners\s*\(\s*\)\s*\{(.*?)\n\}",
+        _JS,
+        re.DOTALL,
+    )
+    assert match, "bindStaticEventListeners function not found"
+    body = match.group(1)
+    assert "new-session-fab" in body, (
+        "bindStaticEventListeners must reference 'new-session-fab'"
+    )
+
+
+def test_js_open_session_hides_fab() -> None:
+    """openSession must add 'hidden' class to the FAB element."""
+    match = re.search(
+        r"async function openSession\s*\(.*?\)\s*\{(.*?)\n\}",
+        _JS,
+        re.DOTALL,
+    )
+    assert match, "openSession function not found"
+    body = match.group(1)
+    assert "new-session-fab" in body, (
+        "openSession must reference 'new-session-fab' to hide FAB during fullscreen view"
+    )
+    assert "hidden" in body, (
+        "openSession must add 'hidden' class to FAB (classList.add('hidden'))"
+    )
+
+
+def test_js_close_session_restores_fab() -> None:
+    """closeSession must remove 'hidden' class from the FAB element."""
+    match = re.search(
+        r"function closeSession\s*\(\s*\)\s*\{(.*?)\n\}",
+        _JS,
+        re.DOTALL,
+    )
+    assert match, "closeSession function not found"
+    body = match.group(1)
+    assert "new-session-fab" in body, (
+        "closeSession must reference 'new-session-fab' to restore FAB when session closed"
+    )
+    assert "remove" in body, (
+        "closeSession must call classList.remove('hidden') on FAB"
+    )
+
+
+def test_js_fab_exported() -> None:
+    """new-session-fab binding functions must work - showNewSessionInput is exported."""
+    assert "showNewSessionInput" in _JS, (
+        "showNewSessionInput must exist in app.js (used by FAB click handler)"
+    )