We have studied a three-dimensional time-dependent quantum dynamics of He - O2 inelastic scattering by using a recently published ab initio potential energy surface. The state-to-state transition probabilities at zero total angular momentum have been calculated in the energy range of 0.12-0.59 eV, and the product rotational distributions are extracted. J-shifting approximation is used to estimate the probabilities for J > 0. The integral cross sections and thermal rate constants are then calculated.