The auto-berthing of a ship requires excellent control for safe accomplishment. Crabbing, which is the pure sway motion of a ship without surge velocity, can be used for this purpose. Crabbing is induced by a peculiar operation procedure known as the push-pull mode. When a ship is in the push-pull mode, an interacting force is induced by complex turbulent flow around the ship generated by the propellers and side thrusters. In this paper, three degrees of freedom equations of the motions of crabbing are derived. The equations are used to apply the adaptive backstepping control method to the auto-berthing controller of a cruise ship. The controller is capable of handling the system non-linearity and uncertainty of the berthing process. A control allocation algorithm for a ship equipped with two propellers and two side thrusters is also developed, the performance of which is validated by simulation of auto-berthing.