A radial basis function neural network sliding-mode controller (RBFSMC) is proposed to control a shape memory alloy (SMA) actuator. This approach, which combines a RBF neural network with sliding-mode control (SMC), is presented for the tracking control of a class of nonlinear systems having parameter uncertainties. The centers and output weights of the RBF neural network are updated through on-line learning, which causes the output of the neural network control to approximate the sliding-mode equivalent control along the direction that makes the sliding-mode asymptotically stable. Using Lyapunov theory, the asymptotic stability of the overall system is proven. Then, the controller is applied to compensate for the hysteresis phenomenon seen in SMA. The results show that the controller was applied successfully. The control results are also compared to those of a conventional SMC.