Long-span cable-stayed bridges are subjected to the risk of collision from passing ships. Conducting experimental study on the collision of bridges and vessels is difficult due to high cost and limited space. In this paper, the behavior of a 1[Formula: see text]018-m long-span cable-stayed bridge subjected to ship collisions is numerically studied. Finite element models of the entire bridge and ships are established. Four different dead weight tonnages (DWT), namely, 2[Formula: see text]700, 12[Formula: see text]000, 30[Formula: see text]000, and 75[Formula: see text]000[Formula: see text]t, with impact velocities of 1[Formula: see text]m/s to 6[Formula: see text]m/s are investigated. The complete collision process under different loading scenarios is simulated, from which the collision force, bridge responses and local damage are obtained. The calculated collision force is significantly affected by the impact velocity and DWT, and exhibits a linear relationship with the impact velocity. Comparison with design codes shows that different codes vary significantly in estimating the collision force and Eurocode provides most accurate results. The effect of the material model on the collision force is also studied. This numerical study provides a reference for the ship collision design of long-span cable-stayed bridges.