Graphene is well-known to be two-dimensional material made of carbon atoms. Graphene is the basic material to form nanotube, fullerene and graphite. Graphene is a substance that attracts attention not only as parts of the nanocarbons but also for its own interesting electronic and mechanic properties ( T. Ando, A. K. Geim et.al, K.S. Novoselov et.al). In the last decade, the most significant problem is how to make wide and high quality graphene itself. Nowadays, good quality graphene can be made in labolatories, for example, using SiC(0001) surface. Thus, one of the next step of the research related to graphene is how to make nano structures on graphene plane (V. M. Karphan et.al ). Recently, H.Fujioka et al. has suceeded for the growth of GaN on graphite using PLD (Pulsed Laser Deposition) method and they success to make light emission diode using GaN on graphite (K. Ueno et.al, A. Kobayashi et.al 2006, A. Kobayashi et.al 2007, G. Li et.al, M.-H. Kim et.al, H.Fujioka 2009 ). Since the graphite is made of the stacking of many graphene plane, similar growth will be possible for graphene, if the graphene plane is supported mechanically with the other certain material. Such growth is not limited to GaN, but many other possibilities to form nano structures, nano devices or thin films on graphite plane. In order to apply graphene for such purpose, however, we should first investigate deeply for the interaction between adatoms and graphene plane ( A. Ishii. et.al 2008, K.Nakada et.al). In experiments, the adatom adsroption on graphene is reported for some atomic species (I. Zanella et.a, K. Kong et.al, K. Okazaki et.al, A. Lugo-Solis et.al, M. Wu et.al, H.Gao et.al, J. Dai et.al ) , but not for all atomic species. In this chapter, we introduce the adsorption mechanism, atomic structures, stabilty, migration barriere energies and electronic properties of the adatom adsorption system on graphene plane for most all atomic species using the density functional theory. First, we review briefly the basic properties of graphene used in the following sections as remarks. The band structure of graphene is shown in figure 1. Because of the in-plane hexagonal symmetry, the p