This paper considers the problem of fixed-time synchronization for a class of second-order nonlinear multi-agent systems with a leader-follower architecture.Based on the homogeneous system theory,a new fixed-time synchronization control algorithm is designed such that the synchronization of multiple master-slave coupling systems can be achieved in a fixed time.It is theoretically shown that the synchronization time can be pre-determined which is independent of any initial conditions.Numerical simulations on synchronization of multi-agent systems are finally performed to illustrate the effectiveness of the proposed method.