In order to realize the real-time obstacle avoidance path planning function of unmanned tractors in straight-line operation, this study proposed an obstacle avoidance path planning algorithm that used a fifth degree polynomial function to plan the path based on the improved shortest tangent method. To solve the problems of discontinuous curvature and difficult tracking control of the path planned by the shortest tangent method, firstly, the improved shortest tangent method was used to find the relevant coordinate points. Based on the obtained coordinate points, the fifth degree polynomial function was then used to solve the path. Finally, an obstacle avoidance path with continuous curvature composed of polynomial function curves and straight lines was obtained. The obstacle avoidance path planning algorithm was simulated. The simulation results show that the path generated by the proposed algorithm has features of short distance, good real-time performance and high security. A model predictive controller was designed based on the kinematics model of the Changzhou Dongfeng unmanned tractor, and the obstacle avoidance path planning and tracking control of the unmanned tractor were jointly simulated on the Simulink and CarSim co-simulation platform. The simulation results show that, compared with the improved shortest tangent method, the path planning algorithm based on the fifth degree polynomial function has higher precision and easier tracking control.