Index: clang-tidy/performance/UnnecessaryValueParamCheck.cpp
===================================================================
--- clang-tidy/performance/UnnecessaryValueParamCheck.cpp
+++ clang-tidy/performance/UnnecessaryValueParamCheck.cpp
@@ -128,7 +128,8 @@
     const auto &CurrentParam = *FunctionDecl->getParamDecl(Index);
     Diag << utils::fixit::changeVarDeclToReference(CurrentParam,
                                                            *Result.Context);
-    if (!IsConstQualified)
+    if (!IsConstQualified &&
+        !CurrentParam.getType().getCanonicalType().isConstQualified())
       Diag << utils::fixit::changeVarDeclToConst(CurrentParam);
   }
 }
Index: test/clang-tidy/performance-unnecessary-value-param.cpp
===================================================================
--- test/clang-tidy/performance-unnecessary-value-param.cpp
+++ test/clang-tidy/performance-unnecessary-value-param.cpp
@@ -237,3 +237,12 @@
   ExpensiveToCopyType B;
   B = A;
 }
+
+// Case where parameter in declaration is already const-qualified but not in
+// implementation. Make sure a second 'const' is not added to the declaration.
+void PositiveConstDeclaration(const ExpensiveToCopyType A);
+// CHECK-FIXES: void PositiveConstDeclaration(const ExpensiveToCopyType& A);
+void PositiveConstDeclaration(ExpensiveToCopyType A) {
+  // CHECK-MESSAGES: [[@LINE-1]]:51: warning: the parameter 'A' is copied
+  // CHECK-FIXES: void PositiveConstDeclaration(const ExpensiveToCopyType& A) {
+}