Recently, layered silicon phosphide (SiP) single crystals have been synthesized experimentally. Using the density-functional theory, G(0)W(0) method (G(0): the non-interacting Green's function; W-0: the screened Coulomb interaction) and Bethe-Salpter equation, we explore the feasibility to exfoliate SiP monolayer by modeling the cleavage process, and investigate its electronic, transport, and optical properties. Calculations shows that the cleavage energy of SiP crystal is very small (0.235 J . m(-2)), suggesting that SiP monolayer can be prepared by mechanical exfoliation method. When the number of layers reduces to a monolayer, the indirect gap of SiP becomes a moderate direct gap of 2.880 eV. More interestingly, SiP monolayer exhibits a high hole-mobility of 2, 860 cm(2) . V-1 s(-1). The applied strain on SiP monolayer can effectively tune its gap. Superior optical absorption for near-ultraviolet and visible light is also observed in SiP monolayer. These results demonstrate that SiP monolayer can provide a potential application in novel nano-engineered semiconducting devices.