diff --git a/http2/server.go b/http2/server.go
index 278add72b..c5d081081 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -732,11 +732,7 @@ func isClosedConnError(err error) bool {
 		return false
 	}
 
-	// TODO: remove this string search and be more like the Windows
-	// case below. That might involve modifying the standard library
-	// to return better error types.
-	str := err.Error()
-	if strings.Contains(str, "use of closed network connection") {
+	if errors.Is(err, net.ErrClosed) {
 		return true
 	}