The leader-following consensus of second-order multi-agent systems under the directed network with fixed topology is studied. In order to save network and computing resources, a consensus algorithm via decentralized event- triggered control is proposed. For each following agent, the sampling information is updated and transmitted by properly defined events, which depend on the measurement error. Between two adjacent event times, the control input is only affected by the control signal of the leader. By employing the model transformation method, the matrix theory and the Lyapunov stability theory, some sufficient conditions for the leader-following consensus of second-order multi-agent systems are given. Finally, simulation results show the effectiveness and feasibility of the theoretical results.