We have carried out systematic measurements of the anisotropic magnetic penetration depth λ(T) as a function of oxygen deficiency in YBa 2 Cu 3 O 7 - δ on magnetically aligned powders using a direct AC susceptibility method. The oxygen-depletion range varied from δ = 0 to 0.61. Although, the absolute values of λ(0) for fully oxygenated YBa 2 Cu 3 O 7 - δ are consistent with previous reports, our results show a more rapid increase of the penetration depth in the ab plane, λ a b (0) with δ than previously reported. The temperature dependence of λ(T) is found to obey an AT + BT 2 dependence at low temperatures (0.04 < T/T c < 0.3), which is not expected for conventional s wave superconductors.