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This paper investigates the problem of global asymptotic stabilization of underactuated surface vessels (USVs) whose dynamics features off-diagonal inertia and damping matrices. By using input and state transformations, the dynamic model of USV is converted into an equivalent system consisting of two cascade connected subsystems. For the transformed system, a continuous fractional power control framework is given to achieve global asymptotic stabilization of USVs. Then, the convergence under this framework is analyzed showing that the rate can be improved by adjusting the fractional power term. Finally, a continuous control algorithm is proposed to guarantee the global convergence rate of the USV system. Simulations are given to demonstrate the effectiveness of the presented method.