To improve the accuracy and reliability of orchard spraying robots, an integrated navigation system was developed, consisting of a real-time kinematic positioning-Beidou satellite navigation system (RTK-BDS) receiver, an inertial measurement unit (IMU), a navigation controller, and servo motors. Using the loose coupling combination method, an error Kalman filter algorithm based on the measurement of position and heading angle is implemented to correct the error of the inertial measurement unit in real time. Combining the kinematics model and the pure pursuit model of the spraying robot, a path-tracking control algorithm is proposed. Path planning was conducted according to the terrain characteristics of orchards. Field experiments were carried out on a spraying robot to evaluate the proposed auto-navigation system. The results showed that when the spraying robot was static, the positioning performances of BDS alone and that of the BDS/IMU combined system were similar, the positioning error was less than 1.5 cm, and the heading angle errors were within 0.3°; when the spraying robot moving alone to a straight line at the speed of 0.4 m/s, the position error of the navigation system only using BDS was less than 5.29 cm, the heading angle error was within 3°, while the position error of BDS/IMU integrated navigation system was less than 2.49 cm, and the heading angle error was within 2°. The accuracy of BDS/IMU integrated navigation system is significantly improved. When the orchard spraying robot was moving at the speed of 0.4 m/s, the maximum offset error was lower than 10.77 cm, the average offset error was not higher than 3.55 cm, and the root mean square error (RMSE) of the lateral deviation was 1.19 cm. The results showed that the proposed auto-navigation system could make the spraying robot track the pre-set path smoothly and stably.