Index: include/clang/ASTMatchers/ASTMatchersInternal.h
===================================================================
--- include/clang/ASTMatchers/ASTMatchersInternal.h
+++ include/clang/ASTMatchers/ASTMatchersInternal.h
@@ -746,6 +746,10 @@
 
     if (auto *TD = Node->getAsTagDecl())
       return matchesDecl(TD, Finder, Builder);
+    else if (auto *ET = Node->getAs<ElaboratedType>())
+      return matchesSpecialized(ET->getNamedType(), Finder, Builder);
+    else if (auto *TST = Node->getAs<TemplateSpecializationType>())
+      return matchesSpecialized(*TST, Finder, Builder);
     else if (auto *TT = Node->getAs<TypedefType>())
       return matchesDecl(TT->getDecl(), Finder, Builder);
     // Do not use getAs<TemplateTypeParmType> instead of the direct dyn_cast.
Index: unittests/ASTMatchers/ASTMatchersTraversalTest.cpp
===================================================================
--- unittests/ASTMatchers/ASTMatchersTraversalTest.cpp
+++ unittests/ASTMatchers/ASTMatchersTraversalTest.cpp
@@ -2106,5 +2106,29 @@
                                        functionDecl(hasName("bar"))))));
 }
 
+TEST(HasDeclaration, QualTypeSpecializedTypeAndTemplateSpecializationType) {
+  std::string input =
+      "namespace Namespace {\n"
+      "template<typename T>\n"
+      "class Template {\n"
+      " public:\n"
+      "  void Method() {}\n"
+      "};\n"
+      "}  // namespace Namespace\n"
+      "template <typename U>\n"
+      "void Function(Namespace::Template<U> param) {\n"
+      "  param.Method();\n"
+      "};\n";
+
+  // hasDeclaration should see through:
+  // 1. from ElaboratedType (Namespace::MyTemplate<U>) to
+  //    TemplateSpecializationType (MyTemplate<U>)
+  // 2. from TemplateSpecializationType (MyTemplate<U>)
+  //    to TemplateDecl (MyTemplate<T>).
+  EXPECT_TRUE(matches(input, parmVarDecl(
+      hasName("param"),
+      hasType(qualType(hasDeclaration(decl(anything())))))));
+}
+
 } // namespace ast_matchers
 } // namespace clang