Bandgap engineering is an efficient strategy for controlling the physical properties of semiconductor materials. For flexible two-dimensional (2D) materials, strain provides a nondestructive and adjustable method for bandgap adjustment. Here, we propose that, in 2D materials with out-of-plane ferroelectricity, the antibonding nature of the valence band maximum and conduction band minimum and polarized charge distribution induced by ferroelectricity give rise to giant changes of the bandgap under curvature strain field. This hypothesis was proven by scanning tunneling microscopy/spectroscopy measurements on monolayer α-In2Se3 that revealed that the bandgap of α-In2Se3 increases significantly due to bending. Both experiments and theoretical calculations indicated that the bandgap increases monotonically with the degree of bending of the α-In2Se3 layer. Our work suggests that bending is an effective method for tuning the gaps of 2D ferroelectric materials, providing a new platform for bandgap engineering under the combination of ferroelectricity and strain field.