In response to the fact that autonomous vehicles cannot avoid obstacles by emergency braking alone, this paper proposes an active collision avoidance method for autonomous vehicles based on model predictive control (MPC). The method includes trajectory tracking, adaptive cruise control (ACC), and active obstacle avoidance under high vehicle speed. Firstly, an MPC-based trajectory tracking controller is designed based on the vehicle dynamics model. Then, the MPC was combined with ACC to design the control strategies for vehicle braking to avoid collisions. Additionally, active steering for collision avoidance was developed based on the safety distance model. Finally, considering the distance between the vehicle and the obstacle and the relative speed, an obstacle avoidance function is constructed. A path planning controller based on nonlinear model predictive control (NMPC) is designed. In addition, the alternating direction multiplier method (ADMM) is used to accelerate the solution process and further ensure the safety of the obstacle avoidance process. The proposed algorithm is tested on the Simulink and CarSim co-simulation platform in both static and dynamic obstacle scenarios. Results show that the method effectively achieves collision avoidance through braking. It also demonstrates good stability and robustness in steering to avoid collisions at high speeds. The experiments confirm that the vehicle can return to the desired path after avoiding obstacles, verifying the effectiveness of the algorithm.