CdGd2 （WO4）4 -δ single crystal was grown using the Czochralski＇s method. The crystal structure was tetragonal seheelite with lattice parameters a = b = 0.5203 nm and c = 1. 1359 nm. There were vacancies of （WO4）^2- , therefore, there were some Gd^2＋ ions. Langevin paramagnetism and anisotropy were observed from the δ-T curves at room temperature. The susceptibility X//was 3.5018×10^-3, and X⊥ was 3.4403× 10^-2. The anisotropy was also observed in the electron spin resonance （ESR） experiments. The anisotropic Land6 factors were g//= 2. 1333 and g~ = 2. 8411. The direction of easy magnetization was in the α-b plane. Anisotropic paramagnetic Curie constants C//and C⊥ were not only related to macroscopic a that was observed through the experiment, but were also related to J⊥ and J//, which were the microscopic quantum numbers of the Gd^2＋ and Gd^3｜ ions. Based on the detailed analyses, the proportion of 36.8% of Gd^3＋ ions to 63.2% of Gd^2＋ ions in the Gd ions of the CdGd2（WO4）4-δ crystal was calculated, and δ was 0.638 in the single crystal.
