diff --git a/clang-tools-extra/clang-tidy/modernize/PassByValueCheck.cpp b/clang-tools-extra/clang-tidy/modernize/PassByValueCheck.cpp
--- a/clang-tools-extra/clang-tidy/modernize/PassByValueCheck.cpp
+++ b/clang-tools-extra/clang-tidy/modernize/PassByValueCheck.cpp
@@ -46,8 +46,9 @@
 }
 } // namespace
 
-static TypeMatcher constRefType() {
-  return lValueReferenceType(pointee(isConstQualified()));
+static TypeMatcher notTemplateSpecConstRefType() {
+  return lValueReferenceType(
+      pointee(unless(templateSpecializationType()), isConstQualified()));
 }
 
 static TypeMatcher nonConstValueType() {
@@ -145,16 +146,18 @@
                   // ParenListExpr is generated instead of a CXXConstructExpr,
                   // filtering out templates automatically for us.
                   withInitializer(cxxConstructExpr(
-                      has(ignoringParenImpCasts(declRefExpr(to(
-                          parmVarDecl(
-                              hasType(qualType(
-                                  // Match only const-ref or a non-const value
-                                  // parameters. Rvalues and const-values
-                                  // shouldn't be modified.
-                                  ValuesOnly ? nonConstValueType()
-                                             : anyOf(constRefType(),
-                                                     nonConstValueType()))))
-                              .bind("Param"))))),
+                      has(ignoringParenImpCasts(declRefExpr(
+                          to(parmVarDecl(
+                                 hasType(qualType(
+                                     // Match only const-ref or a non-const
+                                     // value parameters. Rvalues,
+                                     // TemplateSpecializationValues and
+                                     // const-values shouldn't be modified.
+                                     ValuesOnly
+                                         ? nonConstValueType()
+                                         : anyOf(notTemplateSpecConstRefType(),
+                                                 nonConstValueType()))))
+                                 .bind("Param"))))),
                       hasDeclaration(cxxConstructorDecl(
                           isCopyConstructor(), unless(isDeleted()),
                           hasDeclContext(
diff --git a/clang-tools-extra/test/clang-tidy/checkers/modernize-pass-by-value.cpp b/clang-tools-extra/test/clang-tidy/checkers/modernize-pass-by-value.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/modernize-pass-by-value.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/modernize-pass-by-value.cpp
@@ -118,6 +118,26 @@
 J<Movable> j1(Movable());
 J<NotMovable> j2(NotMovable());
 
+template<class T>
+struct MovableTemplateT
+{
+  MovableTemplateT() {}
+  MovableTemplateT(const MovableTemplateT& o) { }
+  MovableTemplateT(MovableTemplateT&& o) { }
+};
+
+template <class T>
+struct J2 {
+  J2(const MovableTemplateT<T>& A);
+  // CHECK-FIXES: J2(const MovableTemplateT<T>& A);
+  MovableTemplateT<T> M;
+};
+
+template <class T>
+J2<T>::J2(const MovableTemplateT<T>& A) : M(A) {}
+// CHECK-FIXES: J2<T>::J2(const MovableTemplateT<T>& A) : M(A) {}
+J2<int> j3(MovableTemplateT<int>{});
+
 struct K_Movable {
   K_Movable() = default;
   K_Movable(const K_Movable &) = default;