Context. The MAGIC collaboration recently reported correlated X-ray and very high-energy (VHE) gamma-ray emission from the gamma-ray binary LS I +61 303 during  ~60% of one orbit. These observations suggest that the emission in these two bands has its origin in a single particle population. Aims. We aim at improving our understanding of the source behaviour by explaining the simultaneous X-ray and VHE data through a radiation model. Methods. We use a model based on a one zone population of relativistic leptonic particles at the position of the compact object and assume dominant adiabatic losses. The adiabatic cooling time scale is inferred from the X-ray fluxes. Results. The model can reproduce the spectra and light curves in the X-ray and VHE bands. Adiabatic losses could be the key ingredient to explain the X-ray and partially the VHE light curves. From the best-fit result we obtain a magnetic field of B ≃ 0.2 G, a minimum luminosity budget of  ~2 × 1035 erg   s-1 and a relatively high acceleration efficiency. In addition, our results seem to confirm that the GeV emission detected by Fermi does not come from the same parent particle population as the X-ray and VHE emission. Moreover, the Fermi spectrum poses a constraint on the hardness of the particle spectrum at lower energies. In the context of our scenario, more sensitive observations would allow us to constrain the inclination angle, which could determine the nature of the compact object.