We studied some new findings on the sliding mode control, that have been derived for the chaos synchronization of memristor – based hyperchaotic Lorenz systems. Nonlinear property has shown that the memristor can be used in chaotic circuits and the latest memristor-based chaotic circuits with different nonlinear equations at times its design attracts quite a lot of attention. The reason why the sliding mode control method is preferred is due to the fact that it is a robust approach and thus less susceptible to the external disturbances. In fact it is affected in a very little range. Numerical simulations of the synchronization of the proposed control methods with the studied system here, have proved to be largely valid.