Aiming at the problem of trajectory tracking in a class of discrete time-varying switched system with arbitrary sequence, in this paper we propose a discrete iterative learning control algorithm. Under the precondition that the switched sequence does not change along the iterative axis but it does along the time axis, this algorithm divides the whole finite time region into several finite subintervals, and uses -norm to prove the convergence strictly, and provides the sufficient convergent condition of the algorithm in the norm form. This method not only realizes the complete tracking for a discrete time-varying switched system within a limited time, but also has a simple structure easy to be realized in engineering. Simulation results verify the validity of the method.