This paper presents the algorithm of a computationally efficient and reliable time-domain numerical tool capable of modelling floating wind turbine (FWT) platforms subjected to waves loads. Validation is performed against the experimental data of the DeepCwind semi-submersible. The platform's responses are modelled according to the Cummins’ equation of motion using frequency-domain hydrodynamic coefficients. Convolution integral of the impulse response functions for radiation forces is modelled using the recursive approach. The Morison equation is implemented to account for the drift force and viscous damping induced by the large heave plate. Mooring lines are modelled according to the lumped mass approach using an adapted version of the op...