In this paper, a new modified of conjugate gradient method named the (HSH) algorithm is presented for solving nonlinear systems of monotone equations (NSME). The main goal is the (HSH) technique can decrease the number of iterations (Ni), the CPU-time (NT), and the number of functions evaluation(Nf), by MATLAB R_2020a and a numerical results comparison with SCG method and PRP method. Under some standard conditions, the well- define and the convergence of the (HSH) algorithm are proved. The numerical experiment indicated the efficiency of the (HSH).