Based on first-principles LCAO method, we study the electronic and atomic structures of DNA nucleobases adenine (A), thymine (T), guanine (G), and cytosine (C) adsorbed on graphene surfaces. The ${pi}-{pi}$ stacking interactions between graphene and nucleobases lead to the bilayer geometries similar to the Bernal stacked graphite. Through the density of states and charge density analyses, it is found that nucleobases are physisorbed on graphene by dispersive interactions with negligible charge exchange. Our calculations reproduce the atomic structures obtained in previous plane wave calculations accurately with much less computation, and well describe the delocalized ${pi}-{pi}$ interactions in graphene-nucleobases system, indicating that the LCAO method is very efficient for investigating graphene-bio systems.