The　calcium　terbium　aluminate　(CaTbAlO4)　single　crystal　was　grown　by　Czochralski　method　successfully　for　the　first　time.　The　structure　of　the　crystal　was　determined　by　X-ray　diffraction　analysis.　The　transmission　spectrum　of　the　crystal　was　measured　at　room　temperature　at　the　wavelength　of　400-1500nm.　The　specific　Faraday　rotation　of　the　single　crystal　was　surveyed　at　room　temperature　at　the　wavelength　532nm,　633nm,　and　1064nm　respectively.　The　Verdet　constants　of　the　CaTbAlO4　crystal　are　calculated　and　the　results　show　that　the　Verdet　constants　of　CaTbAlO4　are　around　110%　higher　than　that　of　TGG　in　the　visible　and　near-infrared　spectral　region.　Therefore,crystal　CaTbAlO4　can　be　promising　material　for　the　fabrication　of　magneto-optical　devices　in　the　visible　region.