To address the motion planning problem of physically connected multi-vessel towing systems, this paper proposes a motion planning approach based on the concept of planning cell. The proposed framework comprises three core components: planning cell, a search strategy, and a planning space. The planning cell serves as a bridge between the continuous dynamics of the towing system and the discrete nature of the search process, enabling the standardization of trajectory segments. By abstracting key constraints such as system heading, waypoints, and navigable areas, a heuristic search strategy is developed to jointly optimize path length and steering efficiency. To ensure completeness of the search, a three-dimensional planning space defined over position and heading is constructed, allowing for re-visitable nodes and guaranteeing that the system arrives at the destination with the desired heading orientation. Simulation results validate that the proposed method can generate safe, efficient, and dynamically feasible trajectories for multi-vessel towing systems under complex dynamic constraints.