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A game theory based trajectory tracking control method is studied for the dual-objective optimization problem of trajectory tracking the accuracy and driving stability of driverless electric formula racing cars in high-speed trajectory conditions. The general control strategy and the model predictive controller based on the evolutionary game between the two players are designed to optimize their own decisions to achieve the optimal payoff for themselves, and to obtain the optimal solution to the dual-objective optimization problem, by taking the dual objectives of trajectory tracking accuracy and driving stability as the two players in the game. Considering the influence of the dynamic environment, the time-varying interactive game mechanism between two plays is introduced, the game payoff matrix is established, the weights of each subject are determined, and a dynamic replication system is constructed by weight evolution to find the optimal equilibrium strategy for the model prediction controller. The simulated results show that the designed controller can play a significant role in optimizing the trajectory tracking accuracy and driving stability compared to a single model predictive controller under different speed tracking conditions.