diff --git a/clang/lib/Sema/SemaCodeComplete.cpp b/clang/lib/Sema/SemaCodeComplete.cpp
--- a/clang/lib/Sema/SemaCodeComplete.cpp
+++ b/clang/lib/Sema/SemaCodeComplete.cpp
@@ -10030,10 +10030,10 @@
         break;
       case llvm::sys::fs::file_type::regular_file: {
         // Only files that really look like headers. (Except in special dirs).
-        // Header extensions from Types.def, which we can't depend on here.
         const bool IsHeader = Filename.endswith_insensitive(".h") ||
                               Filename.endswith_insensitive(".hh") ||
                               Filename.endswith_insensitive(".hpp") ||
+                              Filename.endswith_insensitive(".hxx") ||
                               Filename.endswith_insensitive(".inc") ||
                               (ExtensionlessHeaders && !Filename.contains('.'));
         if (!IsHeader)
diff --git a/clang/test/CodeCompletion/included-files.cpp b/clang/test/CodeCompletion/included-files.cpp
--- a/clang/test/CodeCompletion/included-files.cpp
+++ b/clang/test/CodeCompletion/included-files.cpp
@@ -1,5 +1,5 @@
 // RUN: rm -rf %t && mkdir %t && cp %s %t/main.cc && mkdir %t/a && mkdir %t/QtCore && mkdir %t/Headers %t/Some.framework %t/Some.framework/Headers
-// RUN: touch %t/foo.h && touch %t/foo.cc && touch %t/a/foosys %t/a/foosys.h && touch %t/QtCore/foosys %t/QtCore/foo.h
+// RUN: touch %t/foo.h && touch %t/foo.hxx touch %t/foo.cc && touch %t/a/foosys %t/a/foosys.h && touch %t/QtCore/foosys %t/QtCore/foo.h
 // RUN: touch %t/Headers/foosys %t/Headers/foo.h %t/Some.framework/Headers/foosys %t/Some.framework/Headers/foo.h
 
 // Quoted string shows header-ish files from CWD, and all from system.
@@ -7,51 +7,52 @@
 // RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:6:13 %t/main.cc | FileCheck -check-prefix=CHECK-1 %s
 // CHECK-1-NOT: foo.cc"
 // CHECK-1: foo.h"
+// CHECK-1: foo.hxx"
 // CHECK-1: foosys"
 
 // Quoted string with dir shows header-ish files in that subdir.
 #include "a/foosys"
-// RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:13:13 %t/main.cc | FileCheck -check-prefix=CHECK-2 %s
+// RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:14:13 %t/main.cc | FileCheck -check-prefix=CHECK-2 %s
 // CHECK-2-NOT: foo.h"
 // CHECK-2: foosys.h"
 // CHECK-2-NOT: foosys"
 
 // Angled shows headers from system dirs.
 #include <foosys>
-// RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:20:13 %t/main.cc | FileCheck -check-prefix=CHECK-3 %s
+// RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:21:13 %t/main.cc | FileCheck -check-prefix=CHECK-3 %s
 // CHECK-3-NOT: foo.cc>
 // CHECK-3-NOT: foo.h>
 // CHECK-3: foosys>
 
 // With -I rather than -isystem, the header extension is required.
 #include <foosys>
-// RUN: %clang -fsyntax-only -I %t/a -Xclang -code-completion-at=%t/main.cc:27:13 %t/main.cc | FileCheck -check-prefix=CHECK-4 %s
+// RUN: %clang -fsyntax-only -I %t/a -Xclang -code-completion-at=%t/main.cc:28:13 %t/main.cc | FileCheck -check-prefix=CHECK-4 %s
 // CHECK-4-NOT: foo.cc>
 // CHECK-4-NOT: foo.h>
 // CHECK-4-NOT: foosys>
 
 // Backslash handling.
 #include "a\foosys"
-// RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:34:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-5 %s
+// RUN: %clang -fsyntax-only -isystem %t/a -Xclang -code-completion-at=%t/main.cc:35:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-5 %s
 // CHECK-5: foosys.h"
 
 // Qt headers don't necessarily have extensions.
 #include <foosys>
-// RUN: %clang -fsyntax-only -I %t/QtCore -Xclang -code-completion-at=%t/main.cc:39:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-6 %s
+// RUN: %clang -fsyntax-only -I %t/QtCore -Xclang -code-completion-at=%t/main.cc:40:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-6 %s
 // CHECK-6-NOT: foo.cc>
 // CHECK-6: foo.h>
 // CHECK-6: foosys>
 
 // If the include path directly points into a framework's Headers/ directory, we allow extension-less headers.
 #include <foosys>
-// RUN: %clang -fsyntax-only -I %t/Some.framework/Headers -Xclang -code-completion-at=%t/main.cc:46:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-7 %s
+// RUN: %clang -fsyntax-only -I %t/Some.framework/Headers -Xclang -code-completion-at=%t/main.cc:47:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-7 %s
 // CHECK-7-NOT: foo.cc>
 // CHECK-7: foo.h>
 // CHECK-7: foosys>
 
 // Simply naming a directory "Headers" is not enough to allow extension-less headers.
 #include <foosys>
-// RUN: %clang -fsyntax-only -I %t/Headers -Xclang -code-completion-at=%t/main.cc:53:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-8 %s
+// RUN: %clang -fsyntax-only -I %t/Headers -Xclang -code-completion-at=%t/main.cc:54:13 %t/main.cc -fms-compatibility | FileCheck -check-prefix=CHECK-8 %s
 // CHECK-8-NOT: foo.cc>
 // CHECK-8: foo.h>
 // CHECK-8-NOT: foosys>