Considering the finite-time stability and actuator saturation of the system， two distributed non-smooth control algorithms are designed for the finite-time generalized consensus problem of neutral stable multi-agent system with input saturation under the situation of leaderless and leader following respectively. The algorithm uses local communication between agents to drive agents to reach finite-time generalized consensus. Based on Lyapunov finite-time stability theory， LaSalle invariant set principle， inequality expansion and reduction and matrix knowledge， the sufficient conditions for the multi-agent system to achieve global finite-time generalized consensus and the range of system convergence time are obtained. It is found that the convergence time of the neutral stable multi-agent system with input saturation is related to the control parameters， the communication relationship between agents， the generalized mapping function and the upper bound of saturation function. Finally， numerical simulations verify the correctness and validity of the theoretical results.