In order to study the derailment process and dynamic performance-changing rules of vehicles on a curved track, a method of calculating critical derailment speed is proposed, which is the progressive trial method. In terms of their theoretical basis and calculation results, compared with the two traditional methods (root locus method and limit cycle method) for calculating linear and nonlinear critical speed, the advantages of this method in studying derailment are proved, and its applicable conditions are explained. Taking CRH3 as an example, the critical derailment speed on different radius curves is calculated by the progressive trial method. At the critical derailment speed, the variation laws of wheel lifting, wheel–rail attack angle and dynamic index are analyzed. The discrete elastic contact analysis is used to observe the changes in the wheel–rail contact position and contact spot during derailment. The results show that with the increase in the curve radius and critical speed of derailment, the absolute values of lateral force, vertical forces and derailment coefficient increase at the same position of the line; when the impact angle between the front wheel of the front bogie and the rail increases to more than 0.06 rad, the train is in a critical derailment state.