The wheel–rail interaction will be intensified on account of the complexity of the wheel–rail contact geometry on a curved track. It also may become more complicated and/or have significant difference as the train speed increases, since the dynamic effects cannot be ignored then. In this study, based on explicit Finite Element (FE) software LS-DYNA 971, a Three-Dimensional (3D) elastic-plastic FE model was built to simulate the dynamic wheel–rail contact behaviour of curve negotiating, where the superelevation and roll angle as well as the strain rate effect were considered. The evolution of contact patch and pressure, wheel–rail contact force, the stress/strain state and the acceleration of the axle were employed to examine the wheel–rail transient dynamic response. Furthermore, the influences of axle load, curve radius and strain rate effect were also discussed. It is found that the maximum vertical contact force, contact pressure, stress and strain on the curved track increase with the decreasing curve radius, and they increase with the increasing axle load except for lateral contact force. The wheel–rail dynamic responses on the curved track are significantly enhanced compared to the straight track. Moreover, the strain rate effect can enhance von-Mises stress and contact pressure, suppress the plastic deformation of the rail and wheel, but it has little effect on the vertical and lateral contact forces and stable acceleration of axle. The Rate-Sensitive Factors (RSF) of the wheel and rail on the curved track are weaker than those on the straight track. These findings will be very helpful to study the competitive relationship between the rolling contact fatigue and wear, as well as the crack initiation and propagation problem.