This work addresses adaptive path-following control of underactuated surface vehicles (USV) subject to unknown disturbances. To deal with the underactuation of the vehicle, an arbitrarily small error vector is added to the path-following position error. A disturbance rejection with a time-varying adaptive gain is also used to attenuate the unknown disturbances. A path-following control force is devised to steer the vehicle asymptotically to a small region around the desired path, which can be made arbitrarily small. Uniform asymptotic stability of the path-following is established by Lyapunov stability theory. Simulation results of straight-line following are given to support the theoretical results.