The problem of chaos synchronization between two different chaotic systems with uncertain parameters and nonlinear inputs is investigated. A terminal sliding surface with a faster convergence speed than conventional sliding surface is introduced. Based on the adaptive control theory and the sliding mode control technique, an adaptive sliding mode controller is designed to guarantee the convergence of synchronization errors to the sliding surface and zero equilibrium in finite-time. Finally, numerical simulations about the Lorenz system and the Liu system are carried out, and simulation results show that synchronization errors converge to zero in finite-time, and the effectiveness and applicability of the proposed control scheme is proved adequately.