A mechanism for the H2O2-based epoxidation of olefins catalyzed by the lacunary polyoxometalate (POM) [gamma-(SiO4)W10O32H4]4- (1) has been investigated at the DFT level. In this study, for the first time a "hydroperoxy" mechanism for this important process has been proposed. It is divided into two steps and investigated using the whole lacunary compound as a model. In the first step, a hydroperoxy (W-OOH) species and a water molecule are generated. The formation of this nonradical oxidant (W-OOH), consistent with the experimental suggestions, occurs with a barrier of 4.4 (7.2) kcal/mol (the number without parenthesis includes solvent effects in benzene, while the one with parenthesis is in the gas phase). In the second step, the O-O bond of the W-OOH species is cleaved, and an epoxide is formed. This step has a barrier of 38.7 (40.0) kcal/mol. It was found that the presence of one and two (CH3)4N+ countercations significantly reduces the rate-limiting barrier by 7.6 (8.3) and 11.9 (12.6) kcal/mol, respectively, and makes this lacunary POM a very efficient catalyst for epoxidation of olefins by hydrogen peroxide. It was demonstrated that the lacunary polyoxometalate basically acts as a mononuclear W(VI) complex in activating the oxidant, a conceptually noteworthy finding.