This paper discusses the path-following control of a ship or other floating object by pushing using a single autonomous tugboat. To do this, we first formulate a reduced dynamic equation that contains the dynamics of both the ship and the tugboat without contact force terms, and is expressed by independent variables, such as ship variables (surge, sway, and yaw rates), allowing us to deal with the ship and tugboat as a single system to control the independent variables. It is assumed in this study that the contact between the ship and tugboat is a point contact, and the contact point does not slip. To manipulate the motion of a ship by pushing, the pushing force must be exerted without slipping at the contact point. Thus, the contact force is derived from the dynamic equations of the ship and tugboat and the velocity constraints on the contact point, and its feasible region is defined. This contact force condition is then incorporated into a path-following control method using the reduced dynamic equation to handle the contact force during the pushing operation. The contact force is checked to determine whether it is likely to be exerted outside the feasible region; if so, the control gain used in the path-following control is switched to a smaller value. Simulations under different paths and contact positions are performed, and the results demonstrate that the proposed pushing control method allows the ship to follow a given path correctly while maintaining the contact condition.