Conventional simulation and control methods for sliding-mode control systems are limited by the available sampling bandwidth and allowable tracking error. Consequently, these methods suffer from harmful chattering. This paper presents an adaptive method for the discrete-time simulation and control of sliding-mode control systems, based on an analysis of the relationship between tracking error and sampling rate for these systems. Our analysis shows that the tracking error decreases as the sampling time interval decreases when the sliding condition exists. The adaptive method exploits the concept of discrete-time sliding mode; the method adjusts its sampling rate to ensure that the tracking error is bounded within a boundary layer of the sliding surface. To simulate a sliding-mode system in discrete time, we present an adaptive integration scheme that follows the ideal system within a given tolerance. Likewise, the adaptive method can be used to generate discrete control signals for sliding-mode systems. Simulation results on examples have shown that the adaptive method is free of chattering.