This paper focuses on robust adaptive sliding mode control for a kind of discrete-time state-delay systems with uncertainties and external disturbances.The uncertainties and disturbances are assumed to be norm-bounded but the bound of disturbances and uncertainties of state variables is not necessarily known.Especially,the uncertainties of state variables are mismatched.In this paper,a corresponding adaptive controller is designed by estimating the unknown upper bound of the disturbances and uncertainties of state variables.And it is designed to guarantee that the trajectory of the system can be driven on to the sliding surface in finite time and finally converges into a residual set of the origin.Also,simulation results are presented to illustrate the effectiveness of the control strategy.