With the rapid development of robotics engineering and artificial intelligence, bipedal robots have made significant progress in mimicking the flexibility and agility of bipedal biological creatures. Bipedal robots have broad application potential in industrial, medical and healthcare, and household environments. However, this highly flexible mobility feature places higher demands on the precision and efficiency of the control system, especially in terms of stability and accuracy, which poses challenges to the innovation and optimization of control algorithms. A biped robot motion controller design method integrating zero moment point (ZMP) theory and model predictive control (MPC) strategy is proposed. Based on the basic principles of biped robot kinematics, gait planning was performed using a three-dimensional linear inverted pendulum model, and an MPC-based controller was designed using a table-cart model to optimize ZMP trajectory tracking. This method aims to achieve efficient and stable walking and dynamic balance control of the robot. Simulation verification shows that the proposed controller effectively improves the stability and dynamic adaptability of the robot's walking. By comparing and analyzing the improved ZMP model predictive control algorithm and the basic ZMP model predictive control algorithm, it is found that the robot's walking stability is optimal under the ZMP path planning with double support phase and considering the ZMP preparation phase, and the deviation between the preset ZMP trajectory and the actual ZMP trajectory is the smallest. This study provides a new solution for the gait planning and control of bipedal robots, and verifies the effectiveness of the proposed method through simulation experiments. This not only promotes the development of bipedal robotics, but also provides strong theoretical support and technical guarantee for the development and application of bipedal robotics technology.