It is still unknown nowadays whether magnetic reconnection−-a process occurring both in the magnetotail and at the magnetopause−-can intrinsically accelerate energetic electrons. Observations in the Earth's magnetotail usually indicate strong electron acceleration during magnetic reconnection, while observations at the Earth's magnetopause rarely show such features. With the recently launched Magnetospheric Multiscale (MMS) mission, here we report the first evidence of energetic-electron acceleration at a reconnecting magnetopause. We find that the acceleration of electrons, with energy up to 70 times their thermal energy, occurs in the magnetosheath side of the ion diffusion region and is associated with strong whistler waves. Such acceleration−-not contaminated by the magnetospheric population−-is attributed to nonadiabatic wave-particle interactions, as supported by analyses of the resonance condition. It manifests that energetic-electron acceleration can happen at the reconnecting magnetopause, like that in the tail.