In this paper, we study a leader-following consensus problem with an active leader and distance-determinant topology. In the scenario we consider, only the leader has the information of the desired motion, and only the followers located within a sensing zone can access to the information of the leader. To reach a desired global consensus, a neighbor-based local controller is developed for the followers. We prove that, under some initial conditions, the proposed control scheme can enable the followers to maintain connectivity, avoid collision, and track the varying-velocity leader. Simulations are also presented to illustrate the theoretical results.