Germanene, a germanium analogue of graphene and silicene, has been synthesized on metal substrates. It is predicted that the intrinsic germanene has a Dirac cone in its band structure, just like graphene and silicene. Using first-principles calculations, we investigate the geometrical structures and electronic properties of germanene on the Ag, Au, Cu, Al, Pt and Ir substrates. The Dirac cone of germanene is destroyed on the Al, Pt and Ir substrates but preserved on the Ag and Au substrates with a slight band hybridization. The upper part of the Dirac cone is destroyed for germanene on the Cu substrate while the lower part remains preserved. By contrast, the Dirac cone is always destroyed for silicene on these metal substrates because of a strong band hybridization. Our study suggests that it is possible to extract the intrinsic properties of germanene on the Ag and Au substrates although it appears impossible for silicene on these two substrates.