Index: clang-tidy/misc/CMakeLists.txt
===================================================================
--- clang-tidy/misc/CMakeLists.txt
+++ clang-tidy/misc/CMakeLists.txt
@@ -10,6 +10,7 @@
   MacroParenthesesCheck.cpp
   MacroRepeatedSideEffectsCheck.cpp
   MiscTidyModule.cpp
+  MoveConstantArgumentCheck.cpp
   NoexceptMoveConstructorCheck.cpp
   StaticAssertCheck.cpp
   SwappedArgumentsCheck.cpp
Index: clang-tidy/misc/MiscTidyModule.cpp
===================================================================
--- clang-tidy/misc/MiscTidyModule.cpp
+++ clang-tidy/misc/MiscTidyModule.cpp
@@ -18,6 +18,7 @@
 #include "InefficientAlgorithmCheck.h"
 #include "MacroParenthesesCheck.h"
 #include "MacroRepeatedSideEffectsCheck.h"
+#include "MoveConstantArgumentCheck.h"
 #include "NoexceptMoveConstructorCheck.h"
 #include "StaticAssertCheck.h"
 #include "SwappedArgumentsCheck.h"
@@ -50,6 +51,8 @@
         "misc-macro-parentheses");
     CheckFactories.registerCheck<MacroRepeatedSideEffectsCheck>(
         "misc-macro-repeated-side-effects");
+    CheckFactories.registerCheck<MoveConstantArgumentCheck>(
+        "misc-move-const-arg");
     CheckFactories.registerCheck<NoexceptMoveConstructorCheck>(
         "misc-noexcept-move-constructor");
     CheckFactories.registerCheck<StaticAssertCheck>(
Index: clang-tidy/misc/MoveConstantArgumentCheck.h
===================================================================
--- clang-tidy/misc/MoveConstantArgumentCheck.h
+++ clang-tidy/misc/MoveConstantArgumentCheck.h
@@ -0,0 +1,17 @@
+#include "../ClangTidy.h"
+
+namespace clang {
+namespace tidy {
+namespace misc {
+
+class MoveConstantArgumentCheck : public ClangTidyCheck {
+public:
+  MoveConstantArgumentCheck(StringRef Name, ClangTidyContext *Context)
+      : ClangTidyCheck(Name, Context) {}
+  void registerMatchers(ast_matchers::MatchFinder *Finder) override;
+  void check(const ast_matchers::MatchFinder::MatchResult &Result) override;
+};
+
+} // namespace misc
+} // namespace tidy
+} // namespace clang
Index: clang-tidy/misc/MoveConstantArgumentCheck.cpp
===================================================================
--- clang-tidy/misc/MoveConstantArgumentCheck.cpp
+++ clang-tidy/misc/MoveConstantArgumentCheck.cpp
@@ -0,0 +1,51 @@
+#include "MoveConstantArgumentCheck.h"
+
+#include <iostream>
+using namespace std;
+
+namespace clang {
+namespace tidy {
+namespace misc {
+
+using namespace ast_matchers;
+
+void MoveConstantArgumentCheck::registerMatchers(MatchFinder* Finder) {
+  Finder->addMatcher(
+      callExpr(callee(functionDecl(hasName("::std::move")))).bind("call-move"),
+      this);
+}
+
+void MoveConstantArgumentCheck::check(const MatchFinder::MatchResult& Result) {
+  const auto* CallMove = Result.Nodes.getNodeAs<CallExpr>("call-move");
+  if (CallMove->getNumArgs() != 1) return;
+  const Expr* Arg = CallMove->getArg(0);
+  auto* Context = Result.Context;
+
+  bool IsTypeDependOnTemplateParameter =
+      false;  // my first guess was type->getTypeClass () == 30 but it doesn't
+              // work in some cases. Could you please advice better solution.
+  if (IsTypeDependOnTemplateParameter) return;
+  bool IsConstArg = Arg->getType().isConstQualified();
+  bool IsTriviallyCopyable = Arg->getType().isTriviallyCopyableType(*Context);
+
+  if (IsConstArg || IsTriviallyCopyable) {
+    bool IsVariable = (dyn_cast<DeclRefExpr>(Arg) != nullptr);
+    string message = "std::move of the ";
+    message += IsConstArg ? "const " : "";
+    message += IsVariable ? "variable " : "expression ";
+    message += IsTriviallyCopyable ? "of trivially-copyable type " : "";
+    message += "doesn't have effect. ";
+    message += "Remove std::move()";
+    message += IsConstArg && IsVariable ? " or make the variable non-const." : ".";
+
+    SourceRange RemoveRange1(CallMove->getLocStart(), Arg->getLocStart());
+    SourceRange RemoveRange2(CallMove->getLocEnd(), CallMove->getLocEnd());
+    diag(CallMove->getLocStart(), message)
+        << FixItHint::CreateRemoval(RemoveRange1)
+        << FixItHint::CreateRemoval(RemoveRange2);
+  }
+}
+
+}  // namespace misc
+}  // namespace tidy
+}  // namespace clang
Index: test/clang-tidy/move-const-arg.cpp
===================================================================
--- test/clang-tidy/move-const-arg.cpp
+++ test/clang-tidy/move-const-arg.cpp
@@ -0,0 +1,72 @@
+// RUN: $(dirname %s)/check_clang_tidy.sh %s misc-move-const-arg %t
+// REQUIRES: shell
+
+namespace std {
+// Directly copied from the stl.
+template<typename>
+struct remove_reference;
+
+template<typename _Tp>
+  struct remove_reference
+  { typedef _Tp   type; };
+
+template<typename _Tp>
+  struct remove_reference<_Tp&>
+  { typedef _Tp   type; };
+
+template<typename _Tp>
+  struct remove_reference<_Tp&&>
+  { typedef _Tp   type; };
+
+template<typename _Tp>
+  constexpr typename std::remove_reference<_Tp>::type&&
+  move(_Tp&& __t);
+
+}  // namespace std
+
+class A
+{
+ public:
+  A() {}
+  A(const A& rhs) {}
+  A(A&& rhs) {}
+};
+
+int f1()
+{
+  return std::move(42);
+  // CHECK-MESSAGES: :[[@LINE-1]]:10: warning: std::move of the expression of trivially-copyable type doesn't have effect. Remove std::move().
+  // CHECK-FIXES: return 42;
+}
+
+int f2(int x2)
+{
+  return std::move(x2);
+  // CHECK-MESSAGES: :[[@LINE-1]]:10: warning: std::move of the variable of trivially-copyable type doesn't have effect. Remove std::move().
+  // CHECK-FIXES: return x2;
+}
+
+int* f3(int* x3)
+{
+  return std::move(x3);
+  // CHECK-MESSAGES: :[[@LINE-1]]:10: warning: std::move of the expression of trivially-copyable type doesn't have effect. Remove std::move().
+  // CHECK-FIXES: return x3;
+}
+
+A f4(A x4)
+{
+  return std::move(x4);
+}
+
+A f5(const A x5)
+{
+  return std::move(x5);
+  // CHECK-MESSAGES: :[[@LINE-1]]:10: warning: std::move of the const variable doesn't have effect. Remove std::move() or make the variable non-const.
+  // CHECK-FIXES: return x5;
+}
+
+template<typename T>
+T f6(const T a)
+{
+  return std::move(a);
+}