In order to study the travel behavior of day-to-day path choice under the state of non-equilibrium, based on the prospect theory, we take the randomness of network and limited rationality of path choice into consideration. Based on daily travel experience data, reserved travel time reference points are updated. According to the finite memory rule and travel time updating mechanism, the day-to-day path prospect is calculated. Then, the day-to-day path flow updating rule based on transfer coefficients is established. Finally, we analyze the influence of the proportion of four kinds of travelers (limited rationality, total rationality, total historical information and limited historical information) and the reserved travel time reliability on the evolutionary time of the network to reach the equilibrium state and the final path flow distribution state.