We first consider the effects of the crystal field on both the 4f ground state and the 5d excited state of a Ce3+ ion in the paramagnetic medium CeF3, and further take account of the splitting of the crystalfield ground-state levels caused by the effective superexchange field Hv and the applied field He; then, with a model of a double transition that includes ground-state splitting, we calculate quantitatively the specific Faraday rotation θF, the Verdet constant V, the magnetic susceptibility X, and their temperature dependences in CeF3. Theoretical calculations show 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=-18353(1+63.01/T) in the temperature range 60<T≤300K. The theory is in good agreement with the experimental results.