The development of two-dimensional (2D) photocatalysts with excellent visible light absorption and favorable band alignment is critical for highly-efficient water splitting. Here we systematically study the structural, electronic and optical properties of an experimentally unexplored 2D Silicon Diphosphide (SiP2) based on density functional theory (DFT). We found that the single-layer SiP2 is highly feasible to obtain experimentally by mechanical cleavage and it is dynamically stable by analyzing its vibrational normal mode. Two dimensional SiP2 possesses a direct band gap of 2.25 eV, which is much smaller than those of more widely studied photocatalysts including titania (3.2 eV) and graphitic carbon nitride (2.7 eV), thus displaying excellent ability for sunlight harvesting. Most interestingly, the positions of the conduction band minimum (CBM) and valence band maximum (VBM) in 2D SiP2 fit perfectly the water oxidation and reduction potentials, making it a potential new 2D material that is suitable as a nanoscale photocatalyst for photo-electrochemical water splitting.