This article considers the stochastic user equilibrium(SUE)problem with the route choice behaviour of random regret minimization(RRM).The RRM model contains a regret aversion parameter to quantify the extent to which a traveler evaluates the regret from deselecting the shortest route.Route choice is characterized by a logit formula where the disutility of a route depends on its travel time and the anticipated regret from comparing the travel time with those of all other routes.Notably,we divide the traveler population into multiple classes according to the risk aversion,i.e.,differentiating travelers by their risk aversion parameters.We propose a variational inequality model to formulate the above problem and develop a gradient projection algorithm for its solutions.The proposed model and algorithm are tested by using the Sioux Falls network.