This paper investigates the position and the full-state stabilization problems of an underactuated surface vessel with parameter uncertainties. Two control schemes are proposed with the first one steering the vessel's position and velocity to zero and the second guaranteeing the convergence of all states to zero. The controller design is based on the direct Lyapunov method, the Barbalat's lemma and the sliding-mode technique. In both schemes, the global uniform asymptotic stability of the closed-loop system is achieved despite parameter uncertainties. The effectiveness of the proposed control laws is verified by simulation results.