This paper attempts to study the lane-changing trajectory planning problem of automated vehicles driving on a curved road. The existing models have the following shortcomings. First, the curvature of the curved road is assumed as a constant, while the curvature is a gradient in the real world. Second, the existing studies either do not consider the speed variations of the surrounding vehicles in lane changing or ignore the curvature difference between the target and current lanes. To overcome the shortcomings, this study puts forward a novel trajectory planning model for curved-road lane changing of automated vehicles. In the model, a new strategy of planning a straight-road lane-changing trajectory first and then modifying it to adapt the curvature variation of the curved road is adopted, and a new collision-avoidance model for curved-road lane changing is developed. The proposed model is evaluated by comparing with the existing models and CarSim simulation platform. The results indicate that the proposed model can enhance the curved-road lane-changing safety of automated vehicles, and the lane-changing trajectory planned by the proposed model can be well tracked by automated vehicles.