Radiation damage mechanism of organic–inorganic hybrid perovskites under electron beam irradiation is currently under controversy. First-principles calculations of threshold energies show that the knock-on atomic displacement damage in CH3NH3PbI3 is significant and highly energy-dependent, i.e., for the incident energy below 2.3 keV, knock-on damage is negligible; when the incident energy increases to 2.3, 26.4, 70.4, and 249.4 keV, H, C, N, and I displacements start, respectively; however, Pb does not displace even for 1 MeV incident energy. This finding explains the observation that 5 keV or higher-energy irradiation causes obvious changes in cathodoluminescence spectra while 2 keV causes only small changes. For the 300 keV high energy irradiation used in recent experiments, our results show that the H, C, N, and I knock-on displacements can cause the loss of CH3NH3 and I simultaneously, so the knock-on damage should play an important role in these experiments. The electron diffraction characterization cannot distinguish the CH3NH3 and I loss, so it might give confusing conclusions about damage processes. These results change our fundamental understandings on the radiation-damage mechanisms of CH3NH3PbI3-related perovskites, laying the foundation for the transmission-electron-microscopy characterization of their microscopic structures.