Aerodynamic loads may have effects on the hunting stability, and the factor of curved track makes it more complicated. Therefore, considering the steady aerodynamic loads generated by crosswind and airflow in the opposite advancing direction of train, the hunting stability of high-speed railway vehicle on a curved track is studied in this paper. The changes of gravitational restoring force and creep coefficients which are caused by aerodynamic loads are considered, and the change of equilibrium position due to aerodynamic loads, centrifugal force and the factor of curved track is also in consideration. A mathematical model of a high-speed railway vehicle during curve negotiation with aerodynamic loads is set up. A program based on the model is written and verified. Using this program, the linear critical speed considering the effects of aerodynamic loads is determined by the eigenvalue analysis. This paper investigates the critical speeds in three aerodynamic conditions. Considering the aerodynamic loads, the dependence of critical speed on curve radius and super-elevation is analyzed, and the impact of aerodynamic loads on instability mode is analyzed as well. In addition, this paper obtains the dominant factors affecting critical speed and the variation tendency of critical speed with primary longitudinal stiffness by orthogonal experiments. The results show that the critical speed decreases or increases while the wind is blowing to outer rail or inner rail respectively. The aerodynamic loads produce obvious effects on the instability mode. The variation tendency of critical speed dependence on curve radius in the conditions with aerodynamic loads keeps consistent with the case without aerodynamic loads. It is seen from the orthogonal experiments that, aerodynamic loads and curve radius are the dominant factors affecting linear critical speed of vehicle on a curved track, and the linear critical speed decreases with the increasing of primary longitudinal stiffness.