Floating offshore platforms motions induced by currents are quite complex phenomena, in general. In particular, VIM, Vortex-Induced Motion, is a type often encountered in platforms with circular columns. Recently, VIM has been observed in towing tank tests with a small-scale model of a Floating Offshore Wind Turbine (FOWT), the OC4 Phase II floater, a 3+1 columns platform. The present paper proposes a reduced-order mathematical model (ROM) to assess VIM of a FOWT. The ROM is derived on the horizontal plane, including yaw motions and nonlinear mooring forces. Current forces are represented through ‘wake variables’, adapting phenomenological models firstly used for VIM of mono-column platforms. The ROM is built upon a set of eleven generalized coordinates, three for the rigid body motion on the horizontal plane and a pair of wake variables for each column, resulting in a system of eleven nonlinear second-order ODEs. The pairs of wake variables obey van der Pol equations, and use hydrodynamic coefficients and parameters obtained from previous experiments with small draught cylinders. Hydro-dynamic interferences among columns or heave plates effects on the flow are not considered, for simplicity. The validity of the proposed model is assessed having the mentioned small-scale experimental campaign as a case study. The simulations are carried out at three different current incidence angles, 0, 90 and 180 degrees, spanning a large range of reduced velocities. The simulations reproduce well the oscillations observed in the experimental tests. A good agreement in transverse oscillations is found, including lock-in regions. The simulations also depict a possibly important phenomenon: a resonant yaw motion emerging at high reduced velocities.