diff --git a/clang-tools-extra/clang-tidy/misc/ConstCorrectnessCheck.cpp b/clang-tools-extra/clang-tidy/misc/ConstCorrectnessCheck.cpp
index 7e388201bf79..f07b49444f3e 100644
--- a/clang-tools-extra/clang-tidy/misc/ConstCorrectnessCheck.cpp
+++ b/clang-tools-extra/clang-tidy/misc/ConstCorrectnessCheck.cpp
@@ -23,6 +23,12 @@ namespace {
 // FIXME: This matcher exists in some other code-review as well.
 // It should probably move to ASTMatchers.
 AST_MATCHER(VarDecl, isLocal) { return Node.isLocalVarDecl(); }
+// FIXME: The matcher 'hasName(Name)' asserts that its argument 'Name' is
+// nonempty. Perhaps remove that assertion and replace 'isUnnamed()' with
+// 'hasName("")'.
+AST_MATCHER(VarDecl, isUnnamed) {
+  return Node.getDeclName().isIdentifier() && Node.getName().empty();
+}
 AST_MATCHER_P(DeclStmt, containsAnyDeclaration,
               ast_matchers::internal::Matcher<Decl>, InnerMatcher) {
   return ast_matchers::internal::matchesFirstInPointerRange(
@@ -148,7 +154,7 @@ void ConstCorrectnessCheck::registerMatchers(MatchFinder *Finder) {
 
   if (AnalyzeParameters) {
     const auto ParamMatcher =
-        parmVarDecl(unless(CommonExcludeTypes),
+        parmVarDecl(unless(CommonExcludeTypes), unless(isUnnamed()),
                     anyOf(hasType(referenceType()), hasType(pointerType())))
             .bind("value");
 
diff --git a/clang-tools-extra/docs/clang-tidy/checks/misc/const-correctness.rst b/clang-tools-extra/docs/clang-tidy/checks/misc/const-correctness.rst
index 0365df2aa450..7a0c73e09949 100644
--- a/clang-tools-extra/docs/clang-tidy/checks/misc/const-correctness.rst
+++ b/clang-tools-extra/docs/clang-tidy/checks/misc/const-correctness.rst
@@ -110,15 +110,15 @@ Options
 
   Enable or disable the analysis of function parameters, like
   ``void foo(int* ptr)``. Only reference and pointer parameters are analyzed.
-  Currently, member functions (including constructors) and lambdas are excluded
-  from the analysis. Default is `true`.
+  Unnamed parameters, member functions (including constructors) and lambdas are
+  excluded from the analysis. Default is `true`.
 
   .. code-block:: c++
 
     // Warning
     void function(int& param) {}
     // No warning
-    void function(const int& param) {}
+    void function(const int& param, int&) {}
 
 .. option:: WarnPointersAsValues
 
diff --git a/clang-tools-extra/test/clang-tidy/checkers/misc/const-correctness-parameters.cpp b/clang-tools-extra/test/clang-tidy/checkers/misc/const-correctness-parameters.cpp
index 96d54b844170..8ff099eadb5a 100644
--- a/clang-tools-extra/test/clang-tidy/checkers/misc/const-correctness-parameters.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/misc/const-correctness-parameters.cpp
@@ -509,3 +509,34 @@ void struct_ptr_param_modified(Bar** bp) {
   // CHECK-FIXES: void struct_ptr_param_modified(Bar** const bp) {
   (*bp)->mutating_method();
 }
+
+void unnamed_parameters(int&, char*, Bar, Bar&, int[5]) {
+  // Unnamed parameters are never reported.
+}
+
+void unnamed_and_named_irrelevant_params(const int& X, char*, Bar Z, Bar&, int[5]) {
+  // No report, all parameters are excluded for various reasons.
+}
+
+void unnamed_and_named_params(int& X, int&) {
+  // But a named parameter is reported even if it is next to an unnamed one.
+  // CHECK-MESSAGES: [[@LINE-2]]:31: warning: variable 'X' of type 'int &' can be declared 'const'
+  // CHECK-FIXES: void unnamed_and_named_params(int const& X, int&) {
+}
+
+// If the parameter is named in the definition, its type will be updated in all
+// declarations, inclunding ones where it is unnamed.
+void unnamed_in_decl_named_in_def(int&);
+// CHECK-FIXES: void unnamed_in_decl_named_in_def(int const&);
+
+void unnamed_in_decl_named_in_def(int& X) {
+  // CHECK-MESSAGES: [[@LINE-1]]:35: warning: variable 'X' of type 'int &' can be declared 'const'
+  // CHECK-FIXES: void unnamed_in_decl_named_in_def(int const& X) {
+}
+
+void named_in_decl_unnamed_in_def(int& X);
+
+void named_in_decl_unnamed_in_def(int&) {
+  // If the parameter is unnamed in the definition, it will not be reported, even
+  // if it is named in some declaration.
+}