Index: clang-tools-extra/clang-tidy/bugprone/UseAfterMoveCheck.cpp
===================================================================
--- clang-tools-extra/clang-tidy/bugprone/UseAfterMoveCheck.cpp
+++ clang-tools-extra/clang-tidy/bugprone/UseAfterMoveCheck.cpp
@@ -404,7 +404,8 @@
                hasArgument(0, declRefExpr().bind("arg")),
                anyOf(hasAncestor(lambdaExpr().bind("containing-lambda")),
                      hasAncestor(functionDecl().bind("containing-func"))),
-               unless(inDecltypeOrTemplateArg()))
+               unless(anyOf(inDecltypeOrTemplateArg(),
+                            hasType(qualType(isConstQualified())))))
           .bind("call-move");
 
   Finder->addMatcher(
Index: clang-tools-extra/test/clang-tidy/checkers/bugprone-use-after-move.cpp
===================================================================
--- clang-tools-extra/test/clang-tidy/checkers/bugprone-use-after-move.cpp
+++ clang-tools-extra/test/clang-tidy/checkers/bugprone-use-after-move.cpp
@@ -129,6 +129,14 @@
   // CHECK-NOTES: [[@LINE-3]]:15: note: move occurred here
 }
 
+// Simple case for const value.
+void simpleConst(const A a) {
+  A other_a = std::move(a);
+  a.foo();
+  // CHECK-NOTES-NOT: [[@LINE-1]]:3: warning: 'a' used after it was moved
+  // CHECK-NOTES-NOT: [[@LINE-3]]:15: note: move occurred here
+}
+
 // A warning should only be emitted for one use-after-move.
 void onlyFlagOneUseAfterMove() {
   A a;
@@ -314,8 +322,8 @@
     auto lambda = [a] {
       std::move(a);
       a.foo();
-      // CHECK-NOTES: [[@LINE-1]]:7: warning: 'a' used after it was moved
-      // CHECK-NOTES: [[@LINE-3]]:7: note: move occurred here
+      // CHECK-NOTES-NOT: [[@LINE-1]]:7: warning: 'a' used after it was moved
+      // CHECK-NOTES-NOT: [[@LINE-3]]:7: note: move occurred here
     };
   }
   // This is just as true if the variable was declared inside the lambda.
@@ -721,14 +729,14 @@
     const A a;
     std::move(a);
     passByConstPointer(&a);
-    // CHECK-NOTES: [[@LINE-1]]:25: warning: 'a' used after it was moved
-    // CHECK-NOTES: [[@LINE-3]]:5: note: move occurred here
+    // CHECK-NOTES-NOT: [[@LINE-1]]:25: warning: 'a' used after it was moved
+    // CHECK-NOTES-NOT: [[@LINE-3]]:5: note: move occurred here
   }
   const A a;
   std::move(a);
   passByConstReference(a);
-  // CHECK-NOTES: [[@LINE-1]]:24: warning: 'a' used after it was moved
-  // CHECK-NOTES: [[@LINE-3]]:3: note: move occurred here
+  // CHECK-NOTES-NOT: [[@LINE-1]]:24: warning: 'a' used after it was moved
+  // CHECK-NOTES-NOT: [[@LINE-3]]:3: note: move occurred here
 }
 
 // Clearing a standard container using clear() is treated as a