Path tracking is an important component of autonomous driving and most current path tracking research is based on different positioning sensors, such as GPS, cameras, and LIDAR. However, in certain extreme cases (e.g., in tunnels or indoor parking lots), if these sensors are unavailable, achieving accurate path tracking remains a problem that is worthy of study. This paper addresses this problem by designing a dead reckoning method that is solely reliant on wheel speed for localization. Specifically, a differential drive model is first used for estimating the current relative vehicle position in real time by rear wheel speed, and the deviation between the current path and the reference path is then calculated using the pure pursuit algorithm as a means of obtaining the target steering wheel angle and vehicle speed. The steering wheel and vehicle speed signals are then output by two PID controllers in order to control the vehicle, and the automatic driving path tracking is ultimately realized. Through exhaustive tests and experiments, the stop position error and tracking process error are compared under different conditions, and the effects of vehicle speed, look-ahead distance, starting position angle, and driving mode on tracking accuracy are analyzed. The experimental results show the average error of the end position to be 0.26 m, 0.383 m, and 0.505 m when using BMW-i3 to drive one lap automatically at speeds of 5 km/h, 10 km/h, and 15 km/h in a test area with a perimeter of approximately 200 m.