This paper considers a discrete-time model of a class of multi-agent systems with a leader. We analyze the controllability of the system with fixed and variant (switching) communication topologies, respectively, and obtain necessary and sufficient conditions. The results show that the interconnected systems can be completely controllable even though every subsystem cannot be controllable by appropriately selecting one of the agents as a leader and using switching topology based on neighbor interaction rules. We also present numerical results to illustrate how to control the systems to achieve desired configurations