By performing first principles calculations, we predict a new two-dimensional semiconductor, namely the SnP2S6 monolayer as a potential photocatalyst for solar water splitting. The exfoliation of the SnP2S6 monolayer from the experimentally-known layered bulk crystal is feasible by overcoming a small cleavage energy of 0.24 J m-2. The SnP2S6 monolayer is a stable semiconductor with an indirect band gap of 2.23 eV, which can be effectively tuned by applying an in-plane biaxial strain. In particular, an indirect-to-direct band gap transition can be achieved under compressive strain. The band edge alignments of the monolayer match well with the water redox potentials. The carrier mobility of the SnP2S6 monolayer is as high as 143.12 and 148.48 cm2 V-1 s-1 for holes and electrons, respectively. These extraordinary electronic properties as well as the good light harvesting performance render the SnP2S6 monolayer a good candidate for electronics and a promising photocatalyst to split water.