The effects of graphene stacking are investigated by comparing the results of methane adsorption energy, electronic performance, and the doping feasibility of five dopants (i.e., B, N, Al, Si, and P) via first-principles theory. Both zigzag and armchair graphenes are considered. It is found that the zigzag graphene with Bernal stacking has the largest adsorption energy on methane, while the armchair graphene with Order stacking is opposite. In addition, both the Order and Bernal stacked graphenes possess a positive linear relationship between adsorption energy and layer number. Furthermore, they always have larger adsorption energy in zigzag graphene. For electronic properties, the results show that the stacking effects on band gap are significant, but it does not cause big changes to band structure and density of states. In the comparison of distance, the average interlamellar spacing of the Order stacked graphene is the largest. Moreover, the adsorption effect is the result of the interactions between graphene and methane combined with the change of graphene’s structure. Lastly, the armchair graphene with Order stacking possesses the lowest formation energy in these five dopants. It could be the best choice for doping to improve the methane adsorption.