Working on irregular farmland along a curved path can effectively improve the applicability of unmanned agricultural machinery operations. Aiming at the problem of low coverage of unmanned curved farmland operations, a curved path tracking control method was proposed based on full-state feedback control. A third-order full-state feedback controller with lateral deviation, heading deviation and heading increment as state vectors was constructed. The system was linearized and converted into a spatial matrix form. The gain matrix was solved under the condition of satisfying the system stability constraint to obtain the front wheel steering angle. The front wheel steering angle was compensated according to the curvature of the nearest path point. The controller performance was verified based on the Matlab / Simulink simulation environment. The results showed that the average absolute error after compensation was reduced by 31% compared with that of the algorithm before compensation, and the maximum absolute error was reduced by 17.9% . Three sets of field experiments were designed to verify the proposed method. The test results of variable curvature path showed that when the operating speed of agricultural machinery was 0.7 m/ s, the maximum lateral deviation was 0.070 5 m, the absolute error was 0.021 8 m, the standard deviation was 0.023 4 m, the maximum heading deviation was 12.25°, the absolute error was1.37°, and the standard deviation was 1.68°;the test results of fixed curvature path showed that the maximum lateral deviation was 0.103 4 m, the absolute error was 0.042 4 m, the standard deviation was0.047 7 m, the maximum heading deviation was 8.9°, the absolute error was 1.86°, and the standard deviation was 2.45°;the results of tracking test along curved ridges showed that the maximum lateral deviation was 0.059 7 m, the absolute error was 0.012 3 m, the standard deviation was 0.015 8 m, the maximum heading deviation was 7.01°, the absolute error was 1.85°, and the standard deviation was 2.49°. The tracking accuracy can meet the operational requirements. The research results can provide theoretical and technical support for unmanned agricultural machinery to perform complex and changeable curved edge operations.