The detailed potential energy surfaces (PESs) of poorly understood ion-molecule reactions of CH3O- with O-2(X-3 Sigma(-)(g)) and O-2(a(1)Delta(g)) are accounted for by the density functional theory and ab initio of QCISD and CCSD(T) (single-point) theoretical levels with 6-311++G(d,p) and 6-311++G(3df,2pd) basis sets for the first time. For the reaction of CH3O- with O-2(X-3 Sigma(-)(g)) (R-3), it is shown that a hydrogen-bonded complex (3)1 is initially formed on the triplet PES, which is 1.8 kcal/mol above reactants R-3 at the CCSD(T)//QCISD level, from which all the products P-1-P-8 can be generated. As to the reaction of CH3O- with O-2(a(1)Delta(g)) (R-1), it is found that the two energetically low-lying complexes of (1)1(-31.5 kcal/mol) and (1)2(-24.1 kcal/mol) are initiated on the singlet PES. Starting from them, a total of seven products may be possible, that is, besides P-1, P-2, P-3, P-4, and P-8, which are the same as on the triplet PES, there exist also another two products, P-9 and P-10. For both reactions, taking the thermodynamics and kinetics into consideration, the hydride-transfer species P-1(CH2O + HO2-) should be the most favorable product followed by P-8(e + CH2O + HO2), which is a secondary product of electron-detachment from Pi, and the generation of endothermic P-7(17.7 kcal/mol) for the reaction of CH3O- with O-2(X-3 Sigma(-)(g)) is also possible at high temperature, whereas the remaining products are negligible. The measured branching ratio of products for CH3O- with O-2(X-3 Sigma(-))(g) by Midey et al. is 0.85:0.15 for P-1, and P-8, and that of CH3O- with O-2(a(1)Delta(g)) is 0.52:0.48 with more P-8, which can be rationalized by our theoretical results that P-8 on the triplet PES is 4.9 kcal/mol above R-3, whereas both P-1 and P-8 on the singlet PES are very low-lying at 45.6 and 25.2 kcal/mol below R-1 energetically. The measured total reaction rate constant of CH3O- with O-2(a(1)Delta(g)) is k = 6.9 X 10(-10) cm(3) s(-1) at 300 K, which is larger than that of k = 1.1 x 10(-12) cm(3) s(-1) for the reaction of CH3O- with O-2(X-3 Sigma(-)(g)). This is understandable because both P, and P-8 on the singlet PES can be generated barrierlessly, whereas to give all the products on the triplet PES has to pass the barrier of (3)1 (1.8 kcal/mol) at the CCSD(T)//QCISD level. It is expected that the present theoretical study may be helpful for understanding the reaction mechanisms related to CH3O- and even CH3S-.