Metal-graphene contact is of critical significance in graphene-based nanoelectronics. There are two possible metal-graphene contact geometries: side-contact and end-contact. In this paper, we apply first-principles calculations to study metal-graphene end-contact for these three commonly used electrode metals (Ni, Pd and Ti) and find that they have distinctive stable end-contact geometries with graphene. Transport properties of these metal-graphene-metal (M-G-M) end-contact structures are investigated by density functional theory non-equilibrium Green’s function (DFT-NEGF) algorithm. The Transmission as a function of chemical potential (E-EF) shows asymmetric curves relative to the Fermi level. Transmission curves of Ni-G-Ni and Ti-G-Ti contact structures indicate that bulk graphene sheet is n-doped by Ni and Ti electrodes, but that of Pd-G-Pd shows p-doping of graphene by Pd electrode. The contact behaviors of these electrodes are consistent with experimental observations.