For a class of discrete time-varying multi-agent systems, a topology is made up of virtual leaders and all agents, and a kind of discrete time iterative learning control algorithm is proposed based on the topological structure by introducing a virtual leader to generate the expected trajectory. The algorithm uses the tracking error between each agent and the virtual leader and neighbor during the last iteration, to revise successively the last control law through the combination of the communication weights in the topological structure, and to get the ideal control law. And this paper proves the convergence of the proposed algorithm based on the norm theory, and gives the convergence condition in the sense of $\lambda$-norm. The algorithm can make the output of the discrete time-varying multi-agent completely track the desired trajectory in the finite time interval with the increase of the number of iterations. Both theoretical and simulation results show the effectiveness of the proposed algorithm.