In this paper, the tracking control of a three degree-of-freedom marine vessel is examined. The novelty of this work is the transformation of the asymmetric inertia matrix into a symmetric, positive definite matrix. The asymmetry arises from the added mass common to practical surface vessels and creates a significant challenge for control design. The control design is further complicated by the parametric uncertainties in the dynamic model of the vessel. Two adaptive control schemes with a projection-based adaptation law are proposed: a full-state feedback controller and an output feedback controller. Both controllers are known to yield a uniformly ultimately bounded tracking result in the presence of parametric uncertainty. Numerical simulation results are shown to demonstrate the validity of the proposed controllers.