Mooring line modelling plays an important role in predicting the dynamic response of the floating offshore wind turbines (FOWTs), especially under extreme load conditions. This paper investigates the influence of different mooring line models on the stochastic dynamic responses of a spar-type FOWT. A 16-degree-of-freedom (16-DOF) aero-hydro-servo-elastic model for the spar-type FOWT is first established using Euler-Lagrangian approach, taking into consideration the full coupling of the blade-drivetrain-tower-spar vibrations, a collective pitch controller and a generator controller. Three different mooring line models have been established and incorporated into the 16-DOF model, namely the linear spring model, the quasi-static model and the lumped-mass model, the last of which include the hydrodynamic loads, inertial force and damping force of the mooring cable. Stochastic dynamic analysis of the coupled FOWT-mooring line system is carried out using 3 different turbulent wind conditions and 4 different sea states and a total of 2160 10-min simulations. The mean value, the standard deviation and the extrapolated extreme value of the structural responses (blades, tower and mooring cable) as well as the fatigue equivalent loads are compared for the three different mooring line models.