Crabbing motion is the pure sway motion of a ship without surge velocity. Thus, it can be applied to a berthing operation. Crabbing motion is induced by a peculiar operation method called the push-pull mode. The push-pull mode is induced by using a combination of the main propeller and side thruster. Two propellers generating the same amounts of thrust and rotating in opposite directions produce some yawing moment on a vessel but do not induce longitudinal motion. With the additional operation of side thrusters, the push-pull mode is used to induce a large amount of lateral force. In this paper, three-degree-of-freedom equations of motion such as for the surge, sway, and yaw are constructed for the crabbing motion. Based on these equations of motion, a feedback linearization control method is applied to auto-berthing control for a twin-screw ship with side thrusters. The controller can deal with the nonlinearity of a system, which is present in the berthing maneuver of a twin screw ship. A simulation of the auto-berthing of a ship is performed to validate the performance of the designed controller.