This paper investigates the global chaos synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems (Lü, Chen and Cheng, 2004) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Lü-Chen-Cheng four-scroll chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Lü-Chen-Cheng four-scroll systems.