CeAlO3 crystals were grown in different growth atmospheres by the Czochralski method. The lattice parameters and space group of CeAlO3 crystal were determined by Rietveld structure refinement of X-ray diffraction (XRD) data. The influence of Ce4+ ions in the crystal on the transmittance and crystal color was confirmed by XPS analysis. Magnetization curve at room temperature and temperature dependencies of the magnetic susceptibility in two different directions were measured, indicating that CeAlO3 crystal has remarkable magnetic anisotropy and there is an abnormal magnetic behavior in the vertical <001> direction in the temperature range of 50–150 K. Faraday characteristics of CeAlO3 crystal were investigated at room temperature. Verdet constants of CeAlO3 at 532, 635 and 1064 nm are about 2.1 times as large as those of CeF3. The reason of large Verdet constants was analyzed based on the Van Vleck–Hebb theory and the magnetic circular dichroism (MCD) spectrum.