This paper presents a fast and accurate robust path-following control approach for a fully actuated marine surface vessel in the presence of external disturbances. The path following is realized by simultaneously converging the yaw rate and sway velocity to their respective desired values, which are generated according to the path-following demand. An improved combined control strategy using an integral terminal sliding mode (ITSM) based composite nonlinear feedback (CNF) technique considering the external disturbances, time-varying tracking reference, input saturations and transient performance improvement is proposed in this study. The proposed ITSM-CNF combines the advantages of the CNF control in improving the transient performance and of the ITSM control in guaranteeing good robustness and finite-time convergence. A continuous and smooth sliding mode controller, based on an integral nonsingular terminal sliding surface, is added to the CNF controller to eliminate chattering. The overall stability of the closed-loop system is strictly proved based on the Lyapunov method. Simulations verify the effectiveness of the ITSM-CNF controller in improving the transient path-following performance, inhibiting overshoots, eliminating steady-state errors, rejecting external disturbances and removing chattering effects, considering input saturations, varying path curvature and finite-time convergence.