This paper first considers tne effect or me crystal field on both of tne 4f ground state and 5d excited state of Ce3+ ion in the paramagnetic medium CeF3, and further, takes account of the splitting of the ground state in the crystsl field caused by the effective superexchange field Hv and applied field He, and then using the model of the double transition with ground state splitting, calculates quantitatively the specific Faraday rotation θF, Verdet constant V, magnetic susceptibility X and their temperature dependence in CeF3. A theoretical calculation shows that the magneto-optical effect and its temperature dependence in CeF3 are closely related to the superexchange interaction between Ce3+ ions. V-1 is linearly dependent on T and V/X=-16032(1+68.1/T) in the temperature range 60