The main goal of the present research is to deal with two non-identical hyperchaotic master–slave systems based on an efficient adaptive sliding mode control algorithm, namely the adaptive sliding mode control approach. As long as both non-identical systems are synchronized, the systems mentioned need to be handled through the proposed control algorithm. Since the effect of the external disturbance and uncertainty may truly be ignored, the whole of the chosen states of the slave system should be followed by the corresponding states of the master system in a very careful manner. The proposed adaptive sliding mode control approach has been realized to cope with the synchronization error, in a reasonable amount of time, in order to drive the applicable hyperchaotic systems. Finally, the performance of the proposed control scheme is verified via the simulation results.