A Multi-Agent Motion Prediction and Tracking method based on non-cooperative equilibrium (MPT-NCE) is proposed according to the fact that some multi-agent intelligent evolution methods, like the MADDPG, lack adaptability facing unfamiliar environments, and are unable to achieve multi-agent motion prediction and tracking, although they own advantages in multi-agent intelligence. Featured by a performance discrimination module using the time difference function together with a random mutation module applying predictive learning, the MPT-NCE is capable of improving the prediction and tracking ability of the agents in the intelligent game confrontation. Two groups of multi-agent prediction and tracking experiments are conducted and the results show that compared with the MADDPG method, in the aspect of prediction ability, the MPT-NCE achieves a prediction rate at more than 90%, which is 23.52% higher and increases the whole evolution efficiency by 16.89%; in the aspect of tracking ability, the MPT-NCE promotes the convergent speed by 11.76% while facilitating the target tracking by 25.85%. The proposed MPT-NCE method shows impressive environmental adaptability and prediction and tracking ability.