diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index f126bae84..a3db1ae3c 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -3480,7 +3480,7 @@ void Tokenizer::setVarId()
         std::string varname;
         Token *tok2 = tok ? tok->next() : 0;
         while (tok2) {
-            if (tok2->isName())
+            if (tok2->isName() && tok2->str() != "const")
                 varname = tok2->str();
             else if (tok2->str() != "*" && tok2->str() != "&")
                 break;
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 6e9440ff2..a6aadd3b4 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -186,6 +186,7 @@ private:
         TEST_CASE(varid36);   // ticket #2980 (segmentation fault)
         TEST_CASE(varid37);   // ticket #3092 (varid for 'Bar bar(*this);')
         TEST_CASE(varid38);   // ticket #3272 (varid for 'FOO class C;')
+        TEST_CASE(varid39);   // ticket #3279 (varid for 'FOO::BAR const')
         TEST_CASE(varidFunctionCall1);
         TEST_CASE(varidFunctionCall2);
         TEST_CASE(varidFunctionCall3);
@@ -2955,6 +2956,13 @@ private:
                       tokenizeDebugListing(code));
     }
 
+    void varid39() {
+        const std::string code = "void f(FOO::BAR const);\n";
+        ASSERT_EQUALS("\n\n##file 0\n"
+                      "1: void f ( FOO :: BAR const ) ;\n",
+                      tokenizeDebugListing(code));
+    }
+
     void varidFunctionCall1() {
         const std::string code("void f() {\n"
                                "    int x;\n"