High quality electron beams with flat distributions in both energy and current are critical for many accelerator-based scientific facilities such as free-electron lasers and MeV ultrafast electron diffraction and microscopes. In this Letter, we report on using corrugated structures to compensate for the beam nonlinear energy chirp imprinted by the curvature of the radio-frequency field, leading to a significant reduction in beam energy spread. By using a pair of corrugated structures with orthogonal orientations, we show that the quadrupole wakefields, which, otherwise, increase beam emittance, can be effectively canceled. This work also extends the applications of corrugated structures to the low beam charge (a few pC) and low beam energy (a few MeV) regime and may have a strong impact in many accelerator-based facilities.