In this work, a new conjugate gradient (CG) algorithm named the (H.M.) algorithm is presented as a combination of the search direction and the line search technique for solving nonlinear systems of unconstrained optimization problems. The main goal is to minimize the CPU time (NT2), the iterations number (Ni2) and the function evaluation number (Nf2) of the (H.M.) algorithm this is done through the program MATLAB (with version R2020a) and a numerical results comparison with two methods, (BFGS) and (BMLV) algorithm. Under some criterion circumstances, the well-defined and the convergence of the (H.M.) algorithm are proved, then taking introduction and proceeding to our aim.