This study discusses the asymptotic consensus problem and finite-time leader-following consensus problem of second-order non-linear multi-agent systems (MASs) with directed communication topology. On the basis of the sliding mode control theory, a new distributed asymptotic consensus controller is proposed to ensure that the consensus of MAS can be reached as time goes to infinity. Another finite-time consensus control algorithm is also proposed based on terminal sliding mode control. The finite-time consensus controller can force the states of MAS to achieve the designed terminal sliding mode surface in finite time and maintain on it. The authors also can prove the consensus of MAS can be obtained in finite time on the terminal sliding mode surface if the directed topology has a directed spanning tree. Simulations are given to illustrate the effectiveness of the proposed approaches. © The Institution of Engineering and Technology 2015.