Due to the lack of consideration of heterogeneity in the traditional choice model based on regret theory, there may be errors in interpreting the real choice behavior. Traditional regret functions do not account for the perception of different alternatives and individual socioeconomic characteristics. This paper utilizes Weber’s law to explain the heterogeneity of travelers’ perceptions regarding alternative attributes. It introduces new parameters to consider individual socioeconomic characteristics to improve the classic random regret minimization (RRM) model. Then, these two improvements are incorporated into the model together. Different choice models are established based on random utility maximization (RUM) and RRM, respectively. This paper then takes taxi-hailing choice behavior in Chengdu as an empirical study. The results suggest that the calibration results of different models are consistent, and the overall goodness of fit and hit rate of models under RRM are better than models under RUM. The improved RRM model considering both perception heterogeneity using Weber’s law and socioeconomic characteristics has the best model evaluation indexes. Thus, the improved model could better explain and predict travelers’ choice behavior.