The layered mono-chalcogenide semiconductors MX (M = In, Ga; X = Se, S) have attracted considerable attention due to their high carrier mobility and tunable bandgap, which gives them potential applications in the development of new optoelectronic devices. We have systematically studied the effect of pressure on the band structure evolution and electronic properties of monolayer indium selenide (InSe) using first-principles calculations. The bandgap of monolayer InSe first increases and then decreases with increasing pressure. In addition, monolayer InSe undergoes an indirect to direct bandgap transition at 6.8 GPa. Increasing the pressure further to 10.4 GPa leads to recovery of the indirect bandgap. This indirect-direct bandgap transition is absent in other monolayer MX compounds. The continuous tuning of band structure of monolayer InSe gives them potential applications for pressure-response optoelectronic devices.