This paper investigates the nonlinear hunting stability of a high-speed vehicle on a curved track under steady aerodynamic load. We first established a nonlinear dynamic model of high-speed vehicle on a curved track while considering the effect of aerodynamic load. Then, we wrote a numerical simulation programme and verified the validity. The following two types of aerodynamic conditions were concerned in this study: considering only the aerodynamic lift and considering the crosswind loads. The influence of aerodynamic load on the creep force, the restoring force and moment generated by gravity, and the equilibrium position of the vehicle on the curved track can all change the hunting stability. We calculated bifurcation diagrams, limit cycle motions, nonlinear critical speeds, and frequency spectrum considering those two types of aerodynamic conditions, then compared with those without considering the aerodynamic effects. The results show that multiple frequencies including double frequency, triple frequency, quadruple frequency, and high frequencies will appear in addition to the fundamental frequency when hunting motion occurs. The higher frequencies which are even times of fundamental frequency are caused by the deviation of equilibrium position from track centre, while the deviation of equilibrium position is generated by curve track or crosswind load. Additionally, a positive aerodynamic lift and a crosswind load in the centrifugal direction will decrease the vehicle's motion stability, while a negative aerodynamic lift and a crosswind load in the centripetal direction can improve the stability.