An algorithm of cooperative driving based on model predictive control (MPC) for connected and automated vehicles (CAVs) at non-signalized intersection is proposed in this paper. The intersection and vehicle model is built including the conception of conflict points, the longitudinal vehicle dynamic model, and constraints based on vehicles and traffic. A decentralized model predictive controller is designed to control each CAV crossing the intersection area considering multi-objectives including rear-end collision avoidance at control zone, conflict avoidance at intersection zone, enhancing traffic efficiency, reducing fuel consumption, and improving ride comfort. Simulation results show that with the proposed algorithm, performances of all CAVs at the intersection area have been improved, including performances of safety, traffic efficiency, fuel consumption and comfort. And the proposed algorithm has the potential of practical application.