The marine autonomous surface ship (MASS) has gained significant attention because of its wide application in waterborne transportation in recent years. The trajectory control of the MASS is crucial in ensuring safety, particularly in narrow navigation areas and urgent encounter situations. Model predictive control (MPC) is well known as a sufficient method to solve the tracking problem considering the actuator saturation with model uncertainties and environmental disturbances. However, due to the constraints on computing resources and hardware limits, the controller may fail to find a feasible solution for MPC within a reasonable amount of time, especially when the system models are coupled and complex. To improve the solution efficiency, this paper introduces adaptive constraints to reduce search space for optimization, i.e., the current tracking point’s speed is transformed into input constraints in the MPC formulation to decrease the computation burden, as well as reduce mechanical wear on the thrusters with smaller amplitudes of control actions. Simulations are carried out to evaluate the effectiveness of the proposed method with different MPC forms.