We investigate the electron retroreflection and the Klein tunneling across a graphene-based n–p–n junction irradiated by linearly polarized off-resonant light with the polarization along the x direction. The linearly polarized off-resonant light modifies the band structure of graphene, which leads to the anisotropy of band structure. By adjusting the linearly polarized light and the direction of n–p–n junction simultaneously, the electron retroreflection appears and the anomalous Klein tunneling, the perfect transmission at a nonzero incident angle regardless of the width and height of potential barrier, happens, which arises from the fact that the light-induced anisotropic band structure changes the relation of wavevector and velocity of electron. Our finding provides an alternative and flexible method to modulate electron retroreflection and Klein tunneling.