Two-dimensional (2D) monolayer MoSi₂N₄ has attracted wide attention due to its excellent carrier transport capacity and chemical stability. However, the relationship between its photoelectric properties and applied plane strain has not been thoroughly explored. The effect of plane strain on band structures and photoelectric properties of 2D monolayer MoSi₂N₄ is revealed by the plane-wave ultrasoft pseudopotentials. The results show that the monolayer MoSi₂N₄ is an indirect band gap semiconductor. Its top of valance band is dominated by Mo4d orbitals and partly contributed by N2p orbitals, while its bottom of conduction band is mainly contributed by Mo4d orbitals. Under tensile strain, band gap of monolayer MoSi₂N₄ narrows gradually and effective mass of photogenerated carriers decreases continuously. Under compressive strain, the band gap widens gradually and the effective mass increases slowly. It is worth noting that a compressive strain (ε=-2.8%) results in transition form indirect to direct band gap. Optical absorption of monolayer MoSi₂N₄ exhibits obvious anisotropy, which edge shifts in different degree under the plane strain, effectively expanding the spectral response range of the system and beneficial to the photoelectric properties. These results provide a theoretical guidance for further research on the application of 2D monolayer MoSi₂N₄ in the field of new tunable nano optoelectronic devices.