diff --git a/clang-tools-extra/clang-tidy/readability/ConstReturnTypeCheck.cpp b/clang-tools-extra/clang-tidy/readability/ConstReturnTypeCheck.cpp
--- a/clang-tools-extra/clang-tidy/readability/ConstReturnTypeCheck.cpp
+++ b/clang-tools-extra/clang-tidy/readability/ConstReturnTypeCheck.cpp
@@ -110,9 +110,10 @@
 void ConstReturnTypeCheck::registerMatchers(MatchFinder *Finder) {
   // Find all function definitions for which the return types are `const`
   // qualified, ignoring decltype types.
-  auto NonLocalConstType = qualType(
-      unless(isLocalConstQualified()),
-      anyOf(decltypeType(), autoType(), isTypeOfType(), isTypeOfExprType()));
+  auto NonLocalConstType =
+      qualType(unless(isLocalConstQualified()),
+               anyOf(decltypeType(), autoType(), isTypeOfType(),
+                     isTypeOfExprType(), substTemplateTypeParmType()));
   Finder->addMatcher(
       functionDecl(
           returns(allOf(isConstQualified(), unless(NonLocalConstType))),
diff --git a/clang-tools-extra/test/clang-tidy/checkers/readability/const-return-type.cpp b/clang-tools-extra/test/clang-tidy/checkers/readability/const-return-type.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/readability/const-return-type.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/readability/const-return-type.cpp
@@ -340,3 +340,18 @@
 __typeof__(const int) n21() {
   return 21;
 }
+
+template <typename T>
+struct n25 {
+  T foo() const { return 2; }
+};
+template struct n25<const int>;
+
+template <typename T>
+struct p41 {
+  const T foo() const { return 2; }
+  // CHECK-MESSAGES: [[@LINE-1]]:3: warning: return type 'const
+  // CHECK-MESSAGES: [[@LINE-2]]:3: warning: return type 'const
+  // CHECK-FIXES: T foo() const { return 2; }
+};
+template struct p41<int>;