This paper presents the discrete adaptive sliding mode control of a state-space system in the presence of a bounded disturbance. The delta form of the discrete state-space model is used as it closely resembles that of the continuous model. The control law takes into account of the effect of the disturbance by using its approximate value. The system behavior in the vicinity of the sliding surface is studied. It is shown that the adaptive controller leads to a stable closed-loop system. Also, simulation results are presented to illustrate the features of the proposed adaptive control strategy.