Abstract - In this work, we present a new conjugate gradient method incorporating approach of the hybridization the conjugate gradient update parameters of DY and HS+ convexly which is based on a quasi-Newton philosophy. The computation of the hybrization parameter parameter is obtained by minimizing the distance between the hybrid conjugate gradient direction and the self-scaling memoryless BFGS direction. Our numerical experiments indicate that our proposed method is preferable and in general superior to classical conjugate gradient methods in terms of efficiency and robustness.