Due to travelers' bounded rationality and their differences of risk taking behaviors in route choice, the travelers were divided into four types, who respectively adopted travel time budget (travel time reliability being less than 50%), expected travel time, travel time budget (travel time reliability being more than 50%), and mean-excess travel time as their reference point for route choice. The calculation formulas of the prospect value for four types of travelers when the traffic demand follows a log-normal distribution and the link capacity follows a uniform distribution were derived, and a user equilibrium model was built and formulated as an equivalent variational inequality. The experimental results show that the parameter setting of cumulative prospect theory would have a great impact on the traffic assignment. Specifically, the route prospects of all types of travelers tend to increase with an increase in the gain sensitivity coefficient, and the change of the third and fourth types of travelers is more significant than that of the first and second types of travelers; the route prospects of all types of travelers tend to decrease with an increase in the loss sensitivity coefficient and the loss aversion coefficient, and the change of the first and second types of travelers is more significant than that of the third and fourth types of travelers; as the perception probability coefficient increases, the route prospects of the first and second types of travelers tend to decrease but that of the third and fourth types of travelers tend to increase.