This paper focuses on the dynamic obstacle-avoidance stability problem of bionic quadruped robots and proposes an optimization scheme that integrates Model Predictive Control (MPC) and Dynamic Window Method (DWA). In view of the limitations of the DWA algorithm in avoiding dynamic obstacles, such as insufficient prediction and poor trajectory smoothness, the multi-step prediction capability of MPC is utilized to optimize path planning and speed control. Combined with the verification in the ROS/Gazebo simulation environment and the adaptation of robot motion patterns, the aim is to enhance the safety and stability of robot obstacle-avoidance in complex dynamic environments.