The Faraday rotation caused by electronic transitions between the 4f and 5d states of Ce3+ ions in paramagnetic CeF3 crystals is calculated. The crystal field is an important perturbation on the energy levels. An external magnetic field, together with an additive magnetic field introduced phenomenologically in our paper, would spilt every 4f state into two sublevels. The dipole transitions between these sublevels, and 5d states induce the Faradap effect.The Verdet constant at 0.6328 μm in the temperature range of 60-300 K is obtained. It is shown that our calculation is in good agreement with experiment.