In this paper was to develop method V1-CG methods associated gradient amended to increase the speed of the convergence while retaining the charactenstic mass convergence as the derivation of this method was based on strict convex quadratic function has been develop this way to public function in whichthe supreme derivatives not equal zero. The Desent property and global convergence for the proposed algorithm are established, oure numerical experiment on some test function and it showed us a clear improvement on the way V1-CG modified.