The electron imaging performance of Medipix2 is described. Medipix2 is a hybrid pixel detector composed of two layers. It has a sensor layer and a layer of readout electronics, in which each 55 microm x 55 microm pixel has upper and lower energy discrimination and MHz rate counting. The sensor layer consists of a 300 microm slab of pixellated monolithic silicon and this is bonded to the readout chip. Experimental measurement of the detective quantum efficiency, DQE(0) at 120 keV shows that it can reach approximately 85% independent of electron exposure, since the detector has zero noise, and the DQE(Nyquist) can reach approximately 35% of that expected for a perfect detector (4/pi(2)). Experimental measurement of the modulation transfer function (MTF) at Nyquist resolution for 120 keV electrons using a 60 keV lower energy threshold, yields a value that is 50% of that expected for a perfect detector (2/pi). Finally, Monte Carlo simulations of electron tracks and energy deposited in adjacent pixels have been performed and used to calculate expected values for the MTF and DQE as a function of the threshold energy. The good agreement between theory and experiment allows suggestions for further improvements to be made with confidence. The present detector is already very useful for experiments that require a high DQE at very low doses.