In ship manoeuvrability, the crabbing test is critical to evaluate the hydrodynamic quantities for the guidance of an efficient and safe berthing or unberthing manoeuvres. In the present study, the crabbing performance of a cruise ship is investigated by an unsteady Reynolds-averaged Navier-Stokes (URANS) method considering the instantaneous relative motion between the ship and the quay. In the numerical simulations, the cruise ship is approaching the quay wall at a constant lateral speed. The crabbing motion with five degrees of freedom is modeled by the dynamic overset mesh technique, while the free surface elevation is simulated by the Volume of Fluid method. For reliable predictions of the crabbing performances, the timestep dependency study is conducted and a suitable time step is determined. From the computations, the hydrodynamic performances of the cruise ship, including forces and moments, as well as the surge, sinkage, roll, trim and yaw motions are predicted. The numerical results indicate variations of the hydrodynamic quantities under the impacts of ship speed and blockage effects by the quay wall. The present results can be used to evaluate the crabbing ability of the cruise ship and to provide guidance for estimating and designing the crabbing model test in further investigations.