When a traffic system is abnormal, passengers are prone to blindness, panic, conformity, and other psychological problems. They may thus make incomplete rational decisions. The Multinominal Logit (MNL) model is based on the assumptions of complete information and rationality. It has poor adaptability when used for abnormal situations. Therefore, the incomplete rationality of passengers under abnormal conditions was described using the cumulative prospect theory, and individual differences among passengers were considered to resolve this inability of the classical MNL model. First, the four factors of time, cost, comfort, and convenience were comprehensively considered, and a model was constructed of rail transit nonnormal passenger travel mode selection based on the cumulative prospect theory. It was used to characterize the incomplete rationality of passengers. Afterward, a questionnaire survey was conducted to calibrate the model parameters. Based on the survey results, a differentiated reference point following a Poisson distribution was obtained to describe the reference point dependency phenomenon of the model. The results of a case study indicated that the Poisson distribution test values with the introduction of differentiated reference points met the test criterion of a value that was greater than or equal to 0.05. It explained the essence of passengers' different decisionmaking results and presented a trend of comprehensive prospects fluctuating with the reference points. Finally, this model was compared with the MNL model to verify the rationality of the model. The research results indicated that the model focused on abnormal situations and reflected the incomplete rationality and individual differences of passengers. The overall accuracy was higher than that of the MNL model, and the average absolute error was reduced by 4.9%. The accuracy of the microscopic calculation results was 25.4% better than that of the MNL model. This could provide theoretical support for traffic demand prediction under abnormal rail transit conditions.