This paper first considers the effects of L-S interaction and the crystal field on both the 4Fground state and the 5d excited state of Pr 3+ ions in the paramagnetic material PrF3, and further takes account of the splitting of the crystal-field ground levels caused by the effective superexchange field H Y and the applied field He, and then, using the model of double tramition with the splitting of the ground stale, cabdates quantitatively the magnetic susceptibility x, specific Faraday rotation θF. Verdet constant V. and their temperature dependence in PrF3. The theoretical calculations show that the magneto-optical effect and its temperature dependence in PrF3 are closely related to the superexchange interaction between Pr3+ ions. V-1 and X-1 are linearly dependent of T in the temperature range of [10K≤T≤300K and independent of T in the low-temperature regime. The theory is in agreement with the experimental results.