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Based on the Lyapunov stability theorem, a model reference adaptive sliding mode control scheme is proposed in this paper for a class of multi-input multi-output (MIMO) dynamic systems with mismatched model uncertainties and external disturbances in order to solve robust tracking problems. In this method adaptive mechanisms are employed both in sliding surface function and control effort so that once the dynamics of controlled system enter the designated sliding surface, the trajectories of tracking errors can achieve asymptotic stability even if the mismatched perturbations exist. In addition, with adaptive mechanisms embedded in the proposed control scheme, the controller is able to adapt the unknown upper bound of perturbations without requiring the information of upper bound of perturbations. A numerical example is given for demonstrating the feasibility of the proposed control scheme.