In this paper, a robust adaptive controller for a class of nonlinear uncertain discrete-time systems is developed by combining the backstepping procedures with a simple parameter estimator subject to parameter projection. It is shown that the proposed controller can ensure boundedness of all signals in the overall adaptive systems in the presence of unmodelled dynamics and disturbances. It can also guarantee that the tracking error is bounded by a function of the size of the unmodelled dynamics. In the ideal case when there are no unmodelled dynamics and disturbances, perfect tracking is ensured.