A non-smooth control protocol is proposed in the continuous time domain and the discrete time domain respectively for the consensus problem of second-order directed multi-agent systems. Firstly, a continuous-time non-smooth consensus protocol is proposed. By the Lyapunov theory and homogeneous system theory, it is proved that the finite time consensus of agents' states can be achieved in the absence of external disturbance, and the errors between the agents' states will converge to a range related to the control parameters and external disturbance in the presence of external disturbance. Then, based on sampled-data control, a discrete-time non-smooth consensus protocol is proposed, and the influence of the sampling period on the errors between agents' states is further analyzed, and the explicit expression of the influence of external disturbance, control parameters and the sampling period on the errors of any two agents is given. Finally, a simulation example is given to verify the correctness and effectiveness of the proposed theory.