In this paper, the generalized function projective synchronization of two identical L ü-Chen-Cheng four-scroll chaotic systems is satisfied. Also, we studied the generalized function projective synchronization between two nonidentical chaotic systems, L ü-Chen-Cheng four-scroll chaotic system and new chaotic system, with known parameters. To prove the solutions of the error system that are asymptotic stable, we based on the Lyapunov theorem of stability. The proposed schemes were evaluated through numerical experiments to showcase their effectiveness and impact.