Two-dimensional (2D) materials have been paid great attention due to their unique properties and promising applications in photochemistry and photoelectricity. In this theoretical study, a systematic investigation has been carried out to explore the effect of several isovalent ionic dopants (O, Se, Te, Al, In, Sc and Y) on the electronic structure of GaS monolayer using the HSE06 functionals. Although monodoping with O reduces the band gap of GaS monolayer, its conduction band minimum (CBM) shifts downward below the hydrogen reduction potential, while the band gap remains almost unchanged for monodoping with Se, Te, Al and In dopants. However, the scenario changes on monodoping with Sc and Y dopants, which can effectively narrow the band gap because of shifting up for valence band maximum (VBM) and shifting down for CBM, respectively. In addition, (Sc, Te) and (Y, Te)-codoped GaS monolayers are also investigated. The calculation reveals that band gap is further narrowed for both codoped cases. The extent of band gap narrowing in the case of codoping with (Y, Te) is quite significant (almost 1 eV) to effectively improve the visible light activity of GaS monolayer. Moreover, both codoped systems are more suitable for overall water splitting than that of monodoping systems, which has been confirmed though band edge alignment with respect to water redox levels. However, upon (Sc, Te) codoping system, the CBM mainly stems from 3d orbital of Sc, which is extremely detrimental for improving solar-to-hydrogen conversion efficiency. Fortunately, (Y, Te)-codoped GaS monolayer shows better for water splitting than that of (Sc, Te)-codoping. The calculated optical absorption spectra confirm that (Y, Te)-codoped system has significantly improved visible light absorption. According to the defect formation energy calculation, the formation energies are all negative values except monodoping with In and Te systems, indicating dopants are possible introduced in the experiments. Thus, these findings imply that (Y, Te) is a suitable dopant pair for the controlled band gap engineering of GaS monolayer and (Y, Te)-codoped GaS monolayer should be a promising visible light photocatalyst for water splitting.