In this study, a ship path following control method with roll constraints is proposed utilizing the adaptive line-of-sight (ALOS) method, finite time extended state observer (FTESO) and robust model predictive control (RMPC). ALOS dynamically updates the acceptable radius through waypoints to enhance maneuverability. The FTESO is deployed for estimating ship motion states and external disturbances. In the design of the RMPC controller, input constraints, roll constraints, and infinite time domain performance indicators are integrated into the optimization objectives, reformulated as convex optimization problems expressed as linear matrix inequalities for multi-objective cooperative control. According to Lyapunov stability theory and homogeneity theory, the closed-loop stability and finite-time convergence of the system are ensured. Simulation results indicate that although the proposed method exhibits slightly larger overshoot in path following when reaching extreme angles, the roll reduction rate of the proposed method is 83.40%. Compared with the LOS+MPC method, the proposed method demonstrates a 51.28% improvement in roll reduction rate. The effectiveness and robustness of the proposed control method have been verified, providing valuable references for the design of underactuated ship rudder roll stabilization controllers.