Abstract: With the conditions of active leadership and system topology switching, the leader-following consensus in the second-order nonlinear multi-agent systems is studied. While the protocol takes continuous control at non-pulsed moments and discrete control at pulse moments, an innovative view is raised that the speed increment of each agent is not only related to the displacement state of the adjacency agent but also to the velocity state. A New Model of Error System is constructed, based on Lyapunov stability theory, using mathematical induction and other related knowledge, and getting the sufficient conditions to achieve consensus when the system topology is directed and connected, and the result is verified by the Matlab simulation.