Due to the non-fully-symmetrical configuration, the platform laying angle of semi-submersible floating offshore wind turbines relative to wind/wave load directions has a noticeable influence on the dynamics characteristics of the whole structure, which indicates that the platform mounting orientation should be carefully considered before installation at sea. The directionality effects of short-term wind/wave loads had been discussed in previous studies, which are, however, insufficient to make a full understanding of the directionality impacts. In our study, based on a 25-year met-ocean database, long-term analysis is carried out by means of an efficient frequency-domain model with eight degrees of freedom. The nonlinear quantities such as aerodynamic loads, aerodynamic damping and mooring stiffness are derived from the time-domain simulation tool FAST, serving as a preprocessing database for the frequency-domain model. A case study is carried out by comparing the long-term responses of a Y-shape semi-submersible floating wind turbine in four mounting orientations. Significant differences can be seen. The platform mounted in the most unfavorable orientation tends to suffer from larger peak nacelle acceleration, which would increase the loads and cause higher tower base fatigue damage. These findings highlight the importance of platform mounting orientations and can serve as a basis for the installation of semi-submersible floating wind turbines.