Understanding the manoeuvring performance of a ship requires accurate predictions of the hydrodynamic forces and moments on the ship. In the present study, the hydrodynamic forces and moments on a manoeuvring container ship at various rudder and drift angles are numerically predicted by solving the unsteady Reynolds-averaged Navier-Stokes equations. The effects of dynamic sinkage and trim on the hydrodynamic forces are first investigated together with a grid dependency study to estimate the numerical error and uncertainty caused by grid discretization, and with a validation study combining the experimental data. The results show that the effect of dynamic sinkage and trim is non-negligible, since including it improves the hydrodynamic force predictions and reduces the numerical error and uncertainty, and the averaged error and uncertainty are smaller than the other computational fluid dynamics results where sinkage and trim were fixed with given values from model tests. Therefore, it is included in the subsequent systematic simulations regarding the influence of rudder and drift angles. The computed forces, moments and rudder coefficients at different rudder and drift angles on the container ship are compared with the benchmark model test data. From the computations, all the predicted quantities are in satisfactory agreement with the experimental data. The details of the flow filed and hydrodynamic forces, such as pressure distributions, transverse force distributions along the hull, velocity contours, streamlines and wave patterns are presented and discussed, and a deep insight into the physical mechanism in the hydrodynamic forces on a manoeuvring ship is obtained.