GaP, GaAs, and InP nanowires were grown on graphitic layers by the vapor-liquid-solid method in a metalorganic vapor phase epitaxy chamber. On graphene/SiC(0001), Au particles as catalyst were formed at the steps by controlling the Au deposition rate and the annealing temperature in a low-energy electron microscopy system. GaP nanowires were grown on this substrate, and it was found that vertical nanowires were formed at the steps of the surface. We also performed GaP, GaAs, and InP nanowire growth on graphite substrates. Free-standing nanowires were obtained for all three materials, although they were vertically, diagonally, and laterally-oriented at the same time. The results suggested that the growth at the steps is the key to growing nanowires vertically on graphene surface.