Finite-time distributed cooperative control of a second-order multi-agent system in the form of double integral with unknown leader control inputs is studied.Firstly,in order to estimate the leaders control input information quickly and accurately,a new finite-time tracking differentiator based on hyperbolic tangent function is proposed,and a terminal attractor function is introduced to eliminate chattering.Secondly,a finite-time tracking control law based on a novel variable speed reaching law with deceleration points is designed.The system has faster convergence speed when it is far from the deceleration point,and can effectively reduce the chattering when it is close to the deceleration point.Under the action of this control law,the followers can track the leaders speed and position better by using the obtained control input information.Finally,the simulation results verify the effectiveness of the proposed algorithm.