This paper investigates the dynamic responses of a NREL 5 MW spar-type floating offshore wind turbine (FOWT) under ship collisions. Physics-based finite element models (FEMs) are established by LS-DYNA. Aerodynamics of FOWT are introduced using the steady wind field simulation results. While hydrodynamics of floaters are considered by the MCOL method. The collision forces of ship and vibration frequencies of FOWT match well with the reference values, indicating the rationality of the developed model. Four wind velocities are adopted to represent different operating status for the FOWT. The collision process can be divided into primary and secondary collisions. The maximum force of the secondary collision only has 60% of the primary one. The results show the collision forces with 0 and 7 m/s wind speeds are larger than other cases. This is because the wind thrust delays the collision process through changing the pitch angle of the FOWT. Also, it is observed that the indentation of the spar has the same regular pattern since it is related to the collision force. The secondary collision has almost no effect on the indentation.