An ab initio and direct dynamic study of the reactions of CH3O2 + CH3OH and CH3O2 + CH2OH has been carried out over the temperature range of 300-1500 K. All stationary points were calculated at the MP2/aug-cc-pVTZ level of theory for CH3O2 + CH3OH or at the M06-2X/MG3S level of theory for CH3O2 + CH2OH and identified for the local minimum. The energetic parameters were refined at the QCISD(T)/cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory. For the reaction of CH3OO + CH3OH, two hydrogen abstraction channels producing CH3OOH + CH2OH (R1) and CH3OOH + CH3O (R2) were confirmed. These two channels consist of the same reversible first step involving the formation of a prereactive complex in the entrance channel. The rate constants of these two channels have been calculated by canonical transition station theory (TST) and canonical variational transition station theory (VTST) with Eckart tunneling correction and compared with the available literature data. The positive temperature dependence of the rate constants was observed. The tunneling effect is important at low temperature and decreases with an increase of the temperature. The contribution of R1 to the total rate constant is dominant, with branching ratios of 0.93 at 500 K and 0.67 at 1000 K, although the branching ratio for R2 increases dramatically with the increase of the temperature from 500 K. For the reaction of CH3OO + CH2OH, eight channels were explored on the lowest singlet and triplet surfaces, and an excited intermediate was found to be formed on the singlet surface. A channel proceeding through the formation of an excited intermediate followed by its impulsive dissociation was confirmed as the dominant channels with a branching ratio more than 0.99 in the temperature range of 300-1500 K, where products of CH3O and OCH2OH were given. The rate constant of the dominant channel calculated by multichannel RRKM-VTST is comparable with the available literature data.