Recently, phosphorene electronic and optoelectronic prototype devices have been fabricated with various metal electrodes. We systematically explore for the first time the contact properties of monolayer (ML) phosphorene with a series of commonly used metals (Al, Ag. Cu, Au, Cr, Ni, Ti, and Pd) via both ab initio electronic structure calculations and more reliable quantum transport simulations. Strong interactions are found between all the checked metals, with the energy band structure of ML phosphorene destroyed. In terms of the quantum transport simulations, ML phosphorene forms a n-type Schottky contact with Au, Cu, Cr, Al, and Ag electrodes, with electron Schottky barrier heights (SBHs) of 0.30, 0.34, 0.37, 0.51, and 0.52 eV, respectively, and p-type Schottky contact with Ti, Ni, and Pd electrodes, with hole SBHs of 0.30, 0.26, and 0.16 eV, respectively. These results are in good agreement with available experimental data. Our findings not only provide an insight into the ML phosphorene-metal interfaces but also help in ML phosphorene based device design.