This paper is concentrated on the rate-dependent hysteresis modeling and compensation for a piezoelectric actuator. A least squares support vector machines (LS-SVM) model is proposed and trained by introducing the current input value and input variation rate as the input data set to formulate a one-to-one mapping. After demonstrating the effectiveness of the presented model, a LS-SVM inverse model based feedforward control combined with a PID feedback control is designed to compensate the hysteresis nonlinearity. Simulation results show that the hybrid scheme is superior to either of the stand-alone controllers, and the rate-dependent hysteresis is suppressed to a negligible level, which validate the effectiveness of the constructed controller. Owing to the simple procedure, the proposed modeling and control approaches are expected to be extended to other types of hysteretic systems as well. © 2011 Springer-Verlag.