Effects of non-stoichiometry on anisotropie magnetic states in CuFeO2 with a so-called delafosite structure have been investigated using CuFeO2+δ (δ=-0.061, -0.026, 0.014, 0.085) single crystals. Each single crystal is grown using the floating zone method in each controlled atmosphere and found to have good quality. All crystals show two anisotropie successive antiferromagnetic transitions in the temperature dependence of magnetic susceptibilities. The higher antiferromagnetic transition temperature is not affected by the non-stoichiometry. On the other hand, the lower one shows distinct effects of the non-stoichiometry, depending on the kind of oxygen defects. Oxygen deficiency leads to an increase in TN2, while excess oxygen leads to a decrease. It is also found that all samples show clear anisotropie step anomalies in the magnetization curve up to 38 T and that the anomalies and hystereses depend on the nonstoichiometry.