Axle box bearings (ABBs) are a vital component of a railway locomotive and the reliability determines the operation safety of locomotive. In order to grasp their dynamic behavior during operation, this work theoretically deduces a locomotive–track longitudinal–vertical coupled dynamics model (CDM) that considers detailed dynamics of the ABBs. The model takes into account many complex interactions such as nonlinear contact and friction forces inside the ABB, wheel–rail interactions, and track irregularities. The ABB is coupled with the wheelset and bogie frame separately at each end, thus enabling the integration of the ABB into the locomotive system and a comprehensive study of its dynamic behaviour during the acceleration condition. The results demonstrate that the dynamic interactions within the ABB become more intense as the running speed increases during acceleration, the peak value of contact force between the inner and outer rings increases. Furthermore, as the locomotive speed increases, the traction force decreases, the vertical displacement between the inner and outer rings does not change much, and the longitudinal relative displacement decreases. As a result of this work, it is clear that the operating conditions of the locomotive should be suitably considered in the dynamic assessment, operation and maintenance of locomotive ABBs.