In this paper, we propose an adaptive path tracking algorithm based on the BP (back propagation) neural network to increase the performance of vehicle path tracking in different paths. Specifically, based on the kinematic model of the vehicle, the front wheel steering angle of the vehicle was derived with the PP (Pure Pursuit) algorithm, and related parameters affecting path tracking accuracy were analyzed. In the next step, BP neural networks were introduced and vehicle speed, radius of path curvature, and lateral error were used as inputs to train models. The output of the model was used as the control coefficient of the PP algorithm to improve the accuracy of the calculation of the front wheel steering angle, which is referred to as the BP–PP algorithm in this paper. As a final step, simulation experiments and real vehicle experiments are performed to verify the algorithm’s performance. Simulation experiments show that compared with the traditional path tracking algorithm, the average tracking error of BP–PP algorithm is reduced by 0.025 m when traveling at a speed of 3 m/s on a straight path, and the average tracking error is reduced by 0.27 m, 0.42 m, and 0.67 m, respectively, at a speed of 1.5 m/s with a curvature radius of 6.8 m, 5.5 m, and 4.5 m, respectively. In the real vehicle experiment, an electric patrol vehicle with an autonomous tracking function was used as the experimental platform. The average tracking error was reduced by 0.1 m and 0.086 m on a rectangular road and a large curvature road, respectively. Experimental results show that the proposed algorithm performs well in both simulation and actual scenarios, improves the accuracy of path tracking, and enhances the robustness of the system. Moreover, facing paths with changes in road curvature, the BP–PP algorithm achieved significant improvement and demonstrated great robustness. In conclusion, the proposed BP–PP algorithm reduced the interference of nonlinear factors on the system and did not require complex calculations. Furthermore, the proposed algorithm has been applied to the autonomous driving patrol vehicle in the park and achieved good results.