Straight line path following of the underactuated ONR Tumblehome ship in the presence of ocean currents is studied. The maneuvering modeling group (MMG) model is used to simulate the motion of the vehicle, and a linearized model is constructed for controller design. A guidance strategy combining the line-of-sight (LOS) and integral line-of-sight (ILOS) guidance laws is proposed to compensate for the drift effect. Furthermore, to deal with the saturation of rudder angle and limitation of maximum rudder rate explicitly, the model predictive control (MPC) technology is utilized. Simulations are conducted, and the results show good path following performance of the guidance-based MPC controller.