A novel single-degree-of-freedom multi-frequency model (sdof-mf) for the prediction of the Vortex Induced Vibrations (VIV) of an elastically mounted circular cylinder in two-dimensional cross flow is presented. The proposed model treats the total hydrodynamic force as sum of conventional Morison-like inertia and drag terms related to the cylinder motion in still fluid plus additional harmonics that account for the lift force induced by vortex shedding. Amplitudes, frequencies and phase lags of these harmonics are identified using a Parameter Identification (PI) procedure applied to time domain data of vortex induced forces, here obtained via CFD simulations. The proposed sharp identification via PI of the independent frequencies of the vortex shedding fluid force is the peculiarity of the proposed method. The model is assessed considering a wide range of flow regimes, including lock-in conditions. From the overall results, the proposed sdof-mf model exhibits promising but consistent capabilities in the reproduction of the vortex shedding forces and cylinder motion, in terms of both amplitudes and frequencies.