Adversarial　training　is　believed　to　be　the　most　robust　and　effective　defense　method　against　adversarial　attacks.　Gradientbased　adversarial　attack　methods　are　generally　adopted　to　evaluate　the　effectiveness　of　adversarial　training.　However,　in　this　paper,　by　diving　into　the　existing　adversarial　attack　literature,　we　find　that　adversarial　examples　generated　by　these　attack　methods　tend　to　be　less　imperceptible,　which　may　lead　to　an　inaccurate　estimation　for　the　effectiveness　of　the　adversarial　training.　The　existing　adversarial　attacks　mostly　adopt　gradient-based　optimization　methods　and　such　optimization　methods　have　difficulties　in　searching　the　most　effective　adversarial　examples　(i.e.,　the　global　extreme　points).　On　the　contrast,　in　this　work,　we　propose　a　novel　Non-Gradient　Attack　(NGA)　to　overcome　the　above-mentioned　problem.　Extensive　experiments　show　that　NGA　significantly　outperforms　the　state-of-the-art　adversarial　attacks　on　Attack　Success　Rate　(ASR)　by　2%　similar　to　7%.