Index: clang-tidy/readability/AvoidConstParamsInDecls.cpp
===================================================================
--- clang-tidy/readability/AvoidConstParamsInDecls.cpp
+++ clang-tidy/readability/AvoidConstParamsInDecls.cpp
@@ -36,7 +36,12 @@
       functionDecl(unless(isDefinition()),
                    // Lambdas are always their own definition, but they
                    // generate a non-definition FunctionDecl too. Ignore those.
-                   unless(cxxMethodDecl(ofClass(cxxRecordDecl(isLambda())))),
+                   // Class template instantiations have a non-definition
+                   // CXXMethodDecl for methods that aren't used in this
+                   // translation unit. Ignore those, as the template will have
+                   // already been checked.
+                   unless(cxxMethodDecl(ofClass(cxxRecordDecl(anyOf(
+                       isLambda(), ast_matchers::isTemplateInstantiation()))))),
                    has(typeLoc(forEach(ConstParamDecl))))
           .bind("func"),
       this);
Index: test/clang-tidy/readability-avoid-const-params-in-decls.cpp
===================================================================
--- test/clang-tidy/readability-avoid-const-params-in-decls.cpp
+++ test/clang-tidy/readability-avoid-const-params-in-decls.cpp
@@ -53,6 +53,12 @@
 // CHECK-MESSAGES: :[[@LINE-1]]:10: warning: parameter 'b'
 // CHECK-FIXES: void F12(bool b = true);
 
+template<class T>
+int F13(const bool b = true);
+// CHECK-MESSAGES: :[[@LINE-1]]:9: warning: parameter 'b'
+// CHECK-FIXES: int F13(bool b = true);
+int f13 = F13<int>();
+
 struct Foo {
   Foo(const int i);
   // CHECK-MESSAGES: :[[@LINE-1]]:7: warning: parameter 'i'
@@ -63,6 +69,18 @@
   // CHECK-FIXES: void operator()(int i);
 };
 
+template <class T>
+struct FooT {
+  FooT(const int i);
+  // CHECK-MESSAGES: :[[@LINE-1]]:8: warning: parameter 'i'
+  // CHECK-FIXES: FooT(int i);
+
+  void operator()(const int i);
+  // CHECK-MESSAGES: :[[@LINE-1]]:19: warning: parameter 'i'
+  // CHECK-FIXES: void operator()(int i);
+};
+FooT<int> f(1);
+
 // Do not match on definitions
 void NF1(const int i) {}
 void NF2(const int *const i) {}
@@ -72,6 +90,25 @@
 void NF6(const int *const) {}
 void NF7(int, const int) {}
 void NF8(const int, const int) {}
+template <class T>
+int NF9(const int, const int) { return 0; }
+int nf9 = NF9<int>(1, 2);
+
+// Do not match on inline member functions
+struct Bar {
+  Bar(const int i) {}
+
+  void operator()(const int i) {}
+};
+
+// Do not match on inline member functions of a templated class
+template <class T>
+struct BarT {
+  BarT(const int i) {}
+
+  void operator()(const int i) {}
+};
+BarT<int> b(1);
 
 // Do not match on other stuff
 void NF(const alias_type& i);