In mountainous roads or expressways outside urban areas, curves with complex characteristics such as varying curvature and long continuous mileage are common. These features present significant challenges to the safety of lane-changing and overtaking maneuvers for autonomous vehicles. To address this issue, a path planning method for proactive lane-change overtaking under continuously varying curved conditions. Firstly, at the path planning level, a hybrid control point method is introduced to generate adaptive lane-changing paths by adjusting the lane-change curve. A safety path evaluation model is then constructed to select the optimal path. Secondly, at the speed planning level, based on the optimal path and considering factors such as road curvature, safety, and comfort, constraint conditions are established, and an objective function is formulated to determine the safe driving speed for the vehicle. Finally, a simulation environment is established to validate the planning effectiveness of the proposed method across different curved-road scenarios. The experimental results demonstrate that this method can effectively satisfy the lane-changing and overtaking requirements of vehicles in curved-road scenarios while ensuring vehicle safety.