We report the chemical vapor deposition growth characteristics of graphene on various catalytic metal substrates such as Ni, Fe, Ag, Au, and Pt. 50-nm-thick metal films were deposited on $SiO_2/Si$ substrates using dc magnetron sputtering. Graphene was synthesized on the metal/$SiO_2$/Si substrates with $CH_4$ gas (1 SCCM) diluted in mixed gases of 10% $H_2$ and 90 % Ar (99 SCCM) using inductively-coupled plasma chemical vapor deposition (ICP-CVD). The highest quality of graphene film was achieved on Ni and Fe substrates at $900^{circ}C$ and 500 W of ICP power. Ni substrate seemed to be the best catalytic material among the tested materials for graphene growth because it required the lowest growth temperature ($600^{circ}C$) as well as showing a low ICP power of 200W. Graphene films were successfully grown on Ag, Au, and Pt substrates as well. Graphene was formed on Pt substrate within 2 sec, while graphene film was achieved on Ni substrate over a period of 5 min of growth. These results can be understood as showing the direct CVD growth of graphene with a highly efficient catalytic reaction on the Pt surface.