To deal with the problem of dynamic path planning for autonomous driving with avoidance of obstacles, a real-time dynamic path planning approach was proposed to avoid obstacles in real-time under the condition of knowing initial vehicle position, speed, orientation and the obstacle positions. Firstly, a base frame of the road was constructed using the continuity of the second derivative for cubic spline curves combined with the information of the road edges and lanes. Secondly, the s-q coordinate system was established using the position and orientation of the vehicle and the curvature of the road. Then a set of smooth curves from the current position to the destination were generated as the path candidates in the s-q coordinate system. Finally, considering the factors of safety, smoothness and continuity, a novel cost function was designed, and the optimal path was selected by minimizing the cost function. Various simulative roads were designed to test the proposed method in the experiments. The experimental results show that the proposed approach has the ability of planning a safe and smooth path for avoiding the obstacles on both single-lane roads and multi-lane roads with good real-time performance.