It has been found out that Pd-Co-based catalyst, supported on anodized aluminum, possesses very high activity in combustion reactions of C1–C6 alkanes and toluene. The catalyst characterization has been made by N2-pysisorption, XRD, SEM, XPS, FTIR, TEM, and EPR methods. In view of the great interest, methane combustion was investigated in detail. It is ascertained that the complete oxidation of methane proceeds by dissociative adsorption on PdO and formation of hydroxyl and methyl groups, the former being highly reactive, and it undergoes further reaction to oxygen-containing intermediates, whereupon HCHO is one of them. The presence of Co2+ cations promotes greatly oxygen adsorption. The dissociative adsorption is favored on neighboring Co2+ cations, leading to the formation of bridging peroxides. Further, the oxygen dissociates on the nearest Pd2+ cations. According to the results from the experimental data, instrumental methods, and the observed kinetics and DFT model calculations, it can be concluded that the reaction pathway over Pd+Co/anodic alumina support (AAS) catalyst proceeds most probably through Mars–van Krevelen. The obtained data on the kinetics were used for simulation of the methane combustion in a full-scale adiabatic reactor.