Alumina supported cobalt (Co) and cobalt-iron (CoFe) catalysts are active for CO2 hydrogenation. Different amounts of CO and CH4 are produced depending on the Co and Fe content. The composition of alumina supported CoFe that maximizes the methane yield for the CO2 methanation reaction was determined using statistically defined experiments and response surface methodology. The catalyst that maximized the methane yield contained 21.47 wt% Co and 2.53 wt% Fe on this alumina support. X-ray diffraction and temperature programme reduction studies showed that Fe enhances the reducibility of cobalt oxides to metallic cobalt. Furthermore, transmission electron microscopy with elemental analysis showed uniform distribution of Co and Fe as an evidence of CoFe bimetallic alloy formation. DFT calculations were used to study the adsorption of CO2 and its dissociation into CO and O on Co and CoFe catalysts. A comparison of reaction energy profiles reveals that CO2 dissociation becomes difficult on the CoFe catalyst containing the optimized composition. The experimentally observed increase in methane formation over CoFe catalyst is probably due to this inhibition of CO formation via CO2 dissociation.