AZIMUT project (Spanish CENIT R&D program) is designed to establish the technological groundwork for the subsequent development of a large-scale offshore wind turbine. The project (2010–2013) has analyzed different alternative configurations for the floating offshore wind turbines (FOWT): SPAR, tension leg platform (TLP), and semisubmersible platforms were studied. Acciona, as part of the consortium, was responsible of scale-testing a semisubmersible platform to support a 1.5 MW wind turbine. The geometry of the floating platform considered in this paper has been provided by the Hiprwind FP7 project and is composed by three buoyant columns connected by bracings. The main focus of this paper is on the hydrodynamic modeling of the floater, with especial emphasis on the estimation of the wave drift components and their effects on the design of the mooring system. Indeed, with natural periods of drift around 60 s, accurate computation of the low-frequency second-order components is not a straightforward task. Methods usually adopted when dealing with the slow-drifts of deep-water moored systems, such as the Newman's approximation, have their errors increased by the relatively low resonant periods of the floating system and, since the effects of depth cannot be ignored, the wave diffraction analysis must be based on full quadratic transfer functions (QTFs) computations. A discussion on the numerical aspects of performing such computations is presented, making use of the second-order module available with the seakeeping software wamit®. Finally, the paper also provides a preliminary verification of the accuracy of the numerical predictions based on the results obtained in a series of model tests with the structure fixed in bichromatic waves.