Different Cu contents (x wt%) were supported on the cryptomelane-type manganese oxide octahedral molecular sieve (OMS-2) (xCu/OMS-2; x = 1, 5, 15, and 20) via a pre-incorporation method. Physicochemical properties of the OMS-2 and xCu/OMS-2 samples were characterized by means of the XRD, FT-IR, SEM, TG/DTG, ICP-OES, XPS, O2-TPD, H2-TPR, and in situ DRIFTS techniques, and their catalytic activities were measured for the oxidation of CO, ethyl acetate, and toluene. The results show that the Cu species were homogeneously dispersed in the tunnel and framework structure of OMS-2. Among all of the samples, 15Cu/OMS-2 sample exhibited the best activities with the T50% of 65, 165, and 240 °C as well as the T90% of 85, 215, and 290 °C for CO, ethyl acetate and toluene oxidation, respectively, which was due to the existence of the Cu species and Mn3+/Mn4+ redox couples, rich oxygen vacancies, good oxygen mobility, low-temperature reducibility, and strong interaction between the Cu species and the OMS-2 support. The reaction mechanisms were also deduced by analyzing the in situ DRIFTS spectra of the 15Cu/OMS-2 sample. The excellent oxygen mobility associated with the electron transfer between Cu species and Mn3+/Mn4+ redox couples might be conducive to the continuous replenishment of active oxygen species and the constantly generated reactant intermediates, thereby increasing the reactant reaction rate.