The differential equation of ship motion is built to study the motion of the mooring positioning engineering floating crane under the combined forces of wind, wave and current. The ship motion is numerically simulated to obtain the ship motion response corresponding to the wave parameters and analyzes the wave direction sensitive to the ship response, in order to provide the foundation for the floating crane hoisting work. The results show that a large surge occurs for the floating crane in head sea and following sea, and a large sway occurs in beam sea. However, the overall amplitude of the ship response is small in oblique sea. The oblique waves should be adopted as far as possible for the floating crane under the hoisting operation, in order to avoid too large motion response that affects hoisting. At the same time, the increase of the mooring force can effectively reduce the displacement of the floating crane.