The family of bulk metal phosphorus trichalcogenides (APX3, A = M(II), M(I)(0.5)M(III)(0.5); X = S, Se; M(I), M(II), and M(III) represent Group-I, Group-II, and Group-III metals, respectively) has attracted great attentions because such materials not only own magnetic and ferroelectric properties, but also exhibit excellent properties in hydrogen storage and lithium battery because of the layered structures. Many layered materials have been exfoliated into two-dimensional (2D) materials, and they show distinct electronic properties compared with their bulks. Here we present a systematical study of single-layer metal phosphorus trichalcogenides by density functional theory calculations. The results show that the single layer metal phosphorus trichalcogenides have very low formation energies, which indicates that the exfoliation of single layer APX3 should not be difficult. The family of single layer metal phosphorus trichalcogenides exhibits a large range of band gaps from 1.77 to 3.94 eV, and the electronic structures are greatly affected by the metal or the chalcogenide atoms. The calculated band edges of metal phosphorus trichalcogenides further reveal that single-layer ZnPSe3, CdPSe3, Ag0.5Sc0.5PSe3, and Ag0.5In0.5PX3 (X = S and Se) have both suitable band gaps for visible-light driving and sufficient over-potentials for water splitting. More fascinatingly, single-layer Ag0.5Sc0.5PSe3 is a direct band gap semiconductor, and the calculated optical absorption further convinces that such materials own outstanding properties for light absorption. Such results demonstrate that the single layer metal phosphorus trichalcogenides own high stability, versatile electronic properties, and high optical absorption, thus such materials have great chances to be high efficient photocatalysts for water-splitting.