The precise path-tracking control of tractors and trailers is the key to realizing agricultural automation. In order to improve the path-tracking control accuracy and driving stability of orchard traction spraying robots, this study proposed a navigation path-tracking control algorithm based on Double Deep Q-Network (Double DQN). Drawing on the driver’s driving experience and referring to the principle of radar scanning and the principle of image recognition, a virtual radar model was constructed to generate a virtual radar map. The virtual radar map was used to describe the position relationship between the traction spraying robot and the planned path. Combined with the deep reinforcement learning method, all possible robot driving actions under the current virtual radar map were scored, and the best driving action was selected as the output of the network. In this study, a path-tracking algorithm was self-developed with a deep Q-network trained by driving the traction spraying robot in a simulated virtual environment. The algorithm was tested in both simulations and in a field to follow a typical ‘U’-shaped path. The simulation results showed that the proposed algorithm was able to achieve accurate path-tracking control of the spraying trailer. The field tests showed that when the vehicle speed was 0.36 m/s and 0.75 m/s, the maximum lateral deviation of the algorithm was 0.233 m and 0.266 m, the average lateral deviation was 0.071 m and 0.076 m, and the standard deviation was 0.051 m and 0.057 m, respectively. Compared with the algorithm based on the virtual radar model, the maximum lateral deviation was reduced by 56.37% and 51.54%, the average lateral deviation was reduced by 7.8% and 5.0%, and the standard deviation was reduced by 20.31% and 8.1%, respectively. The results showed that the Double-DQN-based navigation path-tracking control algorithm for the traction spraying robot in the orchard had higher path-tracking accuracy and driving stability, which could meet the actual operational requirements of traditional orchards.