Many single crystals have been developed and commercialized for optical isolators. However, optical isolator materials have been limited to isotropic crystals or to the isotropic direction (optic axis) of anisotropic crystals. This study investigates the wavelength dependences of linear birefringence, linear dichroism, Faraday rotation and magnetic-circular dichroism in a single crystal rare-earth fluoride, namely CeF3. Measurements were made in the direction parallel and perpendicular to the optic axis under an applied magnetic field. The magnetic field was generated by Nd-Fe-B magnets installed in the generalized-high accuracy universal polarimeter (G-HAUP). The first application of G-HAUP to a magneto-optical material is presented. In the CeF3 crystal, the Verdet constants along directions parallel and perpendicular to the optic axis were positive over the measured wavelength region (300–680 nm), and their magnitudes were nearly equal. The success in the accurate measurement on Faraday rotation along anisotropic directions has opened the way to study on optical isolators along the direction other than optic axis.