Index: include/clang/Basic/DiagnosticSemaKinds.td
===================================================================
--- include/clang/Basic/DiagnosticSemaKinds.td
+++ include/clang/Basic/DiagnosticSemaKinds.td
@@ -1966,6 +1966,8 @@
   "use __attribute__((visibility(\"hidden\"))) attribute instead">;
 
 // C++ Concepts TS
+def err_concept_decl_non_template : Error<
+  "'concept' can only appear on the definition of a function template or variable template">;
 def err_concept_decls_may_only_appear_in_namespace_scope : Error<
   "concept declarations may only appear in namespace scope">;
 def err_function_concept_not_defined : Error<
Index: lib/Sema/SemaDecl.cpp
===================================================================
--- lib/Sema/SemaDecl.cpp
+++ lib/Sema/SemaDecl.cpp
@@ -4865,6 +4865,12 @@
     // C++ Concepts TS [dcl.spec.concept]p1: The concept specifier shall be
     // applied only to the definition of a function template or variable
     // template, declared in namespace scope
+    if (!TemplateParamLists.size()) {
+      Diag(D.getDeclSpec().getConceptSpecLoc(),
+           diag::err_concept_decl_non_template);
+      return nullptr;
+    }
+
     if (!DC->getRedeclContext()->isFileContext()) {
       Diag(D.getIdentifierLoc(),
            diag::err_concept_decls_may_only_appear_in_namespace_scope);
Index: test/Parser/cxx-concept-declaration.cpp
===================================================================
--- test/Parser/cxx-concept-declaration.cpp
+++ test/Parser/cxx-concept-declaration.cpp
@@ -25,6 +25,4 @@
 
 template<typename T> concept concept bool C7() { return true; } // expected-warning {{duplicate 'concept' declaration specifier}}
 
-concept D1 = true; // expected-error {{C++ requires a type specifier for all declarations}}
-
-template<concept T> concept bool D2 = true; // expected-error {{unknown type name 'T'}}
+template<concept T> concept bool D1 = true; // expected-error {{unknown type name 'T'}}
Index: test/SemaCXX/cxx-concept-declaration.cpp
===================================================================
--- test/SemaCXX/cxx-concept-declaration.cpp
+++ test/SemaCXX/cxx-concept-declaration.cpp
@@ -15,3 +15,7 @@
 struct C {
   template<typename T> static concept bool D3 = true; // expected-error {{concept declarations may only appear in namespace scope}}
 };
+
+concept bool D4() { return true; } // expected-error {{'concept' can only appear on the definition of a function template or variable template}}
+
+concept bool D5 = true; // expected-error {{'concept' can only appear on the definition of a function template or variable template}}