Collision avoidance plays a vital role in autonomous vehicle systems. As the complexity and scale of missions increase, multi-vehicle systems are adopted in practice. However, there is limited research on collision avoidance of a physically interconnected multi-vessel system. This paper proposes a control scheme for tugboats to tow a ship in congested port areas ensuring collision avoidance that is compliant with COLREGS. The Model Predictive Control (MPC) strategy is used to optimize the towing angles, towing forces, and tugboats' thruster forces and moment. The COLREGS rules are integrated into the ship reference system by altering predefined waypoints to guide the towing system in a safe and lawful way. By designing the cost function for the ship and tugboats in the MPC controller system, the proposed control scheme makes the ship-towing system stay away from the obstacles and follow the calculated waypoints, achieving collision avoidance. Simulation experiments indicate that the proposed method can deal with static and dynamic obstacle situations in complex water traffic environments, and the collision avoidance operations comply with the COLREGS rules.