In this paper, the discrete-time adaptive quasi-sliding mode control for multivariable systems with perturbations and partial model uncertainties is studied. Even though no a priori knowledge of the perturbations is required, the dead-zone function is constructed based on the on-line estimates of the upper bound of the perturbations. By applying the adaptation algorithm with dead-zone, the unknown model parameters are estimated. Then, a discrete quasi-sliding mode adaptive controller with no chattering is synthesized to guarantee the global stability of the closed-loop systems in the sense that all signals remain bounded. If some information of the perturbations is known, the controller can be modified to improve the performance of the controlled systems. Examples and simulation results are presented to illustrate the proposed algorithms.