Strongly　suppressed　recombination　of　electron-hole　pairs,　unexpectedly　high　carrier　mobility,　and　anomalous　optical　response　were　found　in　an　atomically　thin　indium　selenide　(InSe)　photocatalyst.　In　this　study,　we　unraveled　the　photocatalytic　potential　of　two-dimensional　(2D)　InSe-family　group-III　monochalcogenide　MX　(M　=　Ga　and　In　and　X　=　S,　Se,　and　Te)　monolayers　as　water　splitting　hydrogen　production　photocatalysts　on　the　basis　of　density　functional　theory.　Our　results　not　only　highlight　the　high　electron　mobility　and　small　exciton　binding　energy　of　2D　InSe,　but　also　demonstrate　the　energy　evolution　of　the　adsorption　and　decomposition　of　water　molecules　as　well　as　the　hydrogen　production　process　at　the　2D　InSe　surface.　The　excellent　stability　of　the　MX　monolayers　was　confirmed　using　lattice　dynamical　calculations　as　well　as　the　ab　initio　molecular　dynamics　simulations　in　vacuum　and　aqueous　environments.　Moreover,　distinguished　optical　absorption　performance　of　the　MX　monolayers　resulted　in　effective　sunlight　energy　conversion　as　high　as　1.20%,　6.40%,　and　3.22%　for　the　InSe,　InTe,　and　GaTe　monolayers,　respectively.　©　The　Royal　Society　of　Chemistry　2017.