The coordination and cooperative control of networked multi agent systems has many significant applications in the engineering world. This paper investigated the impulsive consensus problem of multi-agent system with an active leader. It is assumed that only one agent of the network updates its state in the impulse manner based on its and the leader’s position at a series of discrete moments. By using tools from matrix theory, numerical analysis and the theory of impulsive differential equation, a simple yet generic criterion was then derived for consensus of the multi agent system. Consequently, computer numerical simulations verify and also visualize the theoretical results, which shows the impacts of the impulsive duration and impulsive strength on the convergence rate.