This paper proposed a new path planning and path following control method for mobile robots based on improved A* algorithm and PID control algorithm, which is suitable for complex maze environments. In the proposed method, the problem of too many turning points of the A* algorithm is solved, and the generated expected path is safe and smooth by extending the obstacles and the fourth-order cubic uniform B-spline optimization method. Afterwards, a PID controller is designed based on the kinematic model of the two-wheel differential robot based on the forward viewpoint. The performance of the proposed method is tested in a specially designed framework. As a verification, detailed experiments are carried out from the two aspects of path planning and path following. The results show that the planning path has few turning points and the path is smooth, and the designed PID controller can control the mobile robot to achieve better path following effect. Finally, the proposed method is validated in a complex maze environment, and the results show that the proposed method enables the robot to traverse the maze without collision.