One popular approach to prepare graphene is to grow them on transition metal substrates via chemical vapor deposition. By using the density functional theory with dispersion correction, we systematically investigate for the first time the interfacial properties of bilayer (BLG) and trilayer graphene (TLG) on metal substrates. Three categories of interfacial structures are revealed. The adsorption of B(T)LG on Al, Ag, Cu, Au, and Pt substrates is a weak physisorption, but a band gap can be opened. The adsorption of B(T)LG on Ti, Ni, and Co substrates is a strong chemisorption, and a stacking-insensitive band gap is opened for the two uncontacted layers of TLG. The adsorption of B(T)LG on Pd substrate is a weaker chemisorption, with a band gap opened for the uncontacted layers. This fundamental study also helps for B(T)LG device study due to inevitable graphene/metal contact.