The finite-time rendezvous control problem is investigated for multi-agent networks where the dynamic of agents is modeled as a second order integrator, the distributed non-smooth bounded control protocol is proposed based on the potential function method and variable structure control idea. Furthermore, it is proved that the nonlinear coupling network can keep connected with its finite initial power. The finite-time stability analysis is made according to the information of second order set-valued Lie derivative of the Lyapunov function and the invariance principle so as to obtain the control scheme that the network can achieve finite-time rendezvous with preserving topology connectivity through choosing suitable pinned weights. Finally, the simulation example is used to illustrate the effectiveness of theoretical results.