Janus indium chalcogenide In₂XY(X, Y = S, Se, and Te where X ≠ Y) monolayers, in analogy to and beyond MoS₂ ones, are proposed to be potential photocatalytic water-splitting catalysts by means of first-principles calculations. The resulting band gaps locate in the visible regime, and the band edges except In₂STe just straddle the H₂O redox potential levels. The carrier mobility and exciton binding energy are higher and smaller than those of MoS₂, respectively. The loose structure and high flexibility allow for the large range of lattice strain applied to respective monolayers. By considering the merits and demerits, we design a compressive strain-driven strategy to boost the water-splitting activity of In₂XY monolayers. Under compressive strain, the valence and conduction band edges shift to higher energies, especially the latter is higher than the hydrogen reduction potential, facilitating hydrogen production, while the band gaps moderately vary still in the visible regime. In the meantime, the carrier mobility of every In₂XY monolayer is enhanced and the exciton binding energy is decreased, improving the reaction kinetics and enhancing the electrochemical performance. We expect that this generic strain-driven band-engineering is also applicable to other two-dimensional materials with good flexibility for photocatalytic water splitting and simultaneously motivates an active line of experimental efforts.