Travelers’ route choice shows bounded-rationality because of different perceptions of route attributes. Based on the bounded-rationality, the paper proposes the dynamic evolution rules and route choice model, and simulation method is applied to study the evolution process and results. The model includes three parameters reflecting the bounded-rationality of travelers. First, simulation results show that the bounded-rationality affects the evolution process. The switching threshold or the perception deviance is larger, convergence rate is faster, and shorter time is needed to reach equilibrium state. Also, fewer perfect rational travelers will lead to similar results. Second, the system can reach equilibrium and the final equilibrium volume of every route is almost unaffected by bounded-rationality. The equilibrium volume of every route is an approximately fixed value under all simulation scenes. At last, it is found that equilibrium volume of every route obeys normal distribution. That is, bounded-rationality affects the equilibrium convergence rate, but volume equilibrium results will not be influenced.