To improve path-following accuracy in curved channel with time-varying non-uniform flow disturbances, this paper proposes a path-following method based on a curvature-adaptive line of sight (LOS) guidance law and composite control. A three-degree-of-freedom ship maneuvering model is established considering the non-uniform flow field. A sliding-window weighted filtering algorithm is employed for the online identification of channel curvature, which informs a curvature-speed coupled adaptive LOS strategy. This strategy dynamically adjusts the look-ahead distance, effectively suppressing tracking overshoot in high-curvature segments. To address time-varying disturbances, an extended state observer (ESO) is introduced to collectively estimate and provide feedforward compensation for disturbances such as wind and current. This is combined with a fuzzy self-tuning proportional-integral-derivative（PID）controller that optimizes parameters in real-time, thereby enhancing the system's robustness against complex disturbances. Simulation results demonstrate that under the tested curved channel conditions, the proposed method achieves a track error of less than 1.2 times the ship's breadth and a root mean square error of heading error below 1.7°, while consistently maintaining a safe distance of over 2.3 times the ship's breadth from the channel boundaries.