Most of the floating wind turbine (FWT) sub-structure concepts are designed with long natural periods of the vertical motions to de-tune from the wave frequency range. The consequence is that the natural frequencies of heave, roll and pitch are excited by low frequency wave and wind loads. The paper focus is on the low frequency (LF) wave drift loads and the related heave and pitch responses of a semi-submersible type of FWT (12MW INO WINDMOOR). It presents several approaches to calculate the wave drift force coefficients and related forces in irregular waves, namely mean wave drift coefficients combined with Newman’s approximation, quadratic transfer functions (QTFs) neglecting the free surface integral from the 2nd order potential flow solution and QTFs based on the full 2nd order solution. The different approximations are used to perform nonlinear time domain simulations of the FWT motions and the results compared to the model test data (the model tests were performed in the ocean basin of SINTEF at a scale of 1:40). The LF damping of heave and pitch is represented by a linear and a quadratic damping coefficient identified from decay model tests. The coupled numerical solution requires a correct representation of the surge mode of motion. In this case, the wave drift forces are represented by empirical QTFs, while the LF damping includes a contribution from the calm water damping represented by a linear and a quadratic coefficient, together with a wave drift damping coefficient. The numerical results show a good agreement with the model test data in irregular waves when full QTFs are used to calculate the wave drift forces.