Criegee intermediates (CIs) play a key role in controlling the atmospheric budget of hydroxyl radical, organic acids, and secondary organic aerosols. In this study, the detailed reaction mechanisms of the simplest Criegee intermediate CH2OO and its derivatives with methane (CH4) have been systematically investigated theoretically. Two pathways A and B have been identified for the title reaction. In pathway A, CIs can act as an oxygen donor by inserting its terminal oxygen atom into the C-H bond of alkanes, resulting in the formation of alcohol species. The corresponding energy barriers ranging from 6.5 to 24.1 kcal/mol are associated with the O-O bond strength of CIs. Meanwhile, this pathway is more favorable thermodynamically, where the free energy changes (enthalpy changes) range from -81.1 (-78.3) to -110.9 (-109.0) kcal/mol, respectively. In pathway B, an addition reaction to produce the hydroperoxides occurs, accompanying the hydrogen transfer from the alkanes to the terminal oxygen atom of CIs. The corresponding energy barriers ranging from 17.3 to 30.9 kcal/mol are higher than those in pathway A. Further calculations of the rate constants suggest that pathway A is the most favorable reaction channel and the rate constant exhibits a positive temperature dependence. In addition, the conformation-dependent reactivity for the title reaction has been observed. The present findings can enable us to better understand the potential reactivity of CIs in the presence of the alkane species.