CdGd2(WO4)4-δ single crystal was grown using the Czochralskis 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 σ-T curves at room temperature. The susceptibility χ// was 3.5018×10-3, and χ⊥ was 3.4403×10-2. The anisotropy was also observed in the electron spin resonance (ESR) experiments. The anisotropic Landé factors were g//=2.1333 and g⊥=2.8411. The direction of easy magnetization was in the a-b plane. Anisotropic paramagnetic Curie constants C// and C⊥ were not only related to macroscopic σ that was observed through the experiment, but were also related to J⊥ 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-δ crystal was calculated, and δ was 0.638 in the single crystal.