CdGd2(WO4)(4-delta)　single　crystal　was　grown　using　the　Czochralski＇s　method.　The　crystal　structure　was　tetragonal　scheelite　with　lattice　parameters　a　=　b　=　0.5203　nm　and　c　=　1.1359　nm.　There　were　vacancies　of　(WO4)(2-),　therefore,　there　were　some　Gd2+　ions.　Langevin　paramagnetism　and　anisotropy　were　observed　from　the　sigma-T　curves　at　room　temperature.　The　susceptibility　chi(//)　was　3.5018　x　10(-3),　and　chi(perpendicular　to)　was　3.4403　x　10(-2).　The　anisotropy　was　also　observed　in　the　electron　spin　resonance　(ESR)　experiments.　The　anisotropic　Lande　factors　were　g(//)　=　2.1333　and　g(perpendicular　to)　=　2.8411.　The　direction　of　easy　magnetization　was　in　the　a-b　plane.　Anisotropic　paramagnetic　Curie　constants　C-//　and　C-perpendicular　to　were　not　only　related　to　macroscopic　a　that　was　observed　through　the　experiment,　but　were　also　related　to　J(perpendicular　to)　and　J(//),　which　were　the　microscopic　quantum　numbers　of　the　Gd2+　and　Gd3+　ions.　Based　on　the　detailed　analyses,　the　proportion　of　36.8%　of　Gd3+　ions　to　63.2%　of　Gd2+　ions　in　the　Gd　ions　of　the　CdGd2(WO4)(4-delta)　crystal　was　calculated,　and　delta　was　0.638　in　the　single　crystal.