The stable GaInSe₂ monolayer as a Janus structure with an indirect band-gap was investigated via first-principles electronic structure calculations. The intrinsic correlation between GaInSe₂ monolayer and its binary analogues (GaSe and InSe monolayers) was investigated in terms of atomic structure and electronic property. The calculation results of atomic structure and phonon frequency dispersion indicate that GaInSe₂ monolayer has a dynamically stable Janus structure with the similar hexagonal geometry as GaSe and InSe monolayers. The electronic band structures show that GaInSe₂ monolayer and its binary analogues are all indirect band-gap semiconductors. It is noted from the strained Janus model that work functions and coherent strains of GaSe and InSe constituents essentially determine the electronic structure of GaInSe₂ monolayer. GaInSe₂ monolayer can be converted into direct band-gap semiconductor when the strain in atomic plane is decreased less than a critical value. Therefore, GaInSe₂ monolayer can be applied to 2-dimensional or surface photoelectric materials under the mechanical conditions below the critical strain. Further, the band-edge character and band-gap width can be effectively controlled by modifying the strains in atomic plane of GaInSe₂ monolayer, which is of great significance for the potential application in field effect nanotransistors.