Travel time and toll cost are two important objectives that travelers want to optimize when choosing a path. Many studies consider these two as a single objective by combining them in linear or nonlinear ways， which has certain defects proved by some researchers. In the studies of static traffic assignment model，some studies have proposed the bi-objective user equilibrium ( BUE) which considers travel time and toll cost separately. However，most studies of dynamic traffic assignment model still consider the traditional single objective user equilibrium as the final stable state of traffic flow evolution. Therefore，a new path-based day-to-day dynamic model with BUE is proposed，assuming that travelers compare the travel time and toll cost separately to decide whether to switch paths each day. The equivalence between the stable state of the proposed dynamic model and BUE state，as well as the convergence of the dynamic model are theoretically proved. Two numerical examples are conducted to verify the effectiveness of the proposed model.