The implementation of expressway toll-free policy during holidays in China has caused serious congestion and frequent accidents on expressways. Many studies have explored the policy's macroscopic outcome and its countermeasures for policy managers, while limited attention has been paid to the influence mechanism of the policy on the individuals' travel behavior, especially the mode choice behavior. More insight into the dynamic effects of individuals reacting to policy measure is needed. This study aims at analyzing the adaption progress of the individual's mode choice behavior and estimating the time-varying influence of the traffic policy on the mode split. With assumptions travelers' adapting behavior conform to the inertia and myopia principles, a Logit dynamic evolutionary model for mode choice is proposed. A unique globally stable equilibrium state for the model is derived with the strict mathematical analysis. As an application, the influence of the expressway toll-free policy on mode split is evaluated. The travel cost structure, the sensitivity of the travel distance and traffic supply, and the evolutionary dynamics of the mode split are analyzed in scenarios with and without the expressway toll-free policy. The result indicates that travel distance and network's total supply amount remarkably affect the implementation effect of the policy.