In this study, the atomic structures and electronic properties of several alkaline earth metals (Ca, Sr and Ba) adsorbed alternately on both sides of graphene are investigated by using first-principles density functional theory (DFT) calculations. These materials are abbreviated to be the Ca-graphene, the Sr-graphene and the Ba-graphene, which contain four atoms in their unit cell (including two alkaline earth metals and two C atoms). The results previously obtained for the pristine graphene, the H-graphene (graphane) and the Li-graphene are resubmitted to check the computational procedure of this study. These results are also used to compare the order of stability of the ones presented here. It is found that alkaline earth metals on graphene we taken into account here show metallic behavior, depending on their electronic band structures and density of states (DOS).