Controlling magnetism by purely electrical means is a key challenge to better information technology(1). A variety of material systems, including ferromagnetic (FM) metals(2-4), FM semiconductors(5), multiferroics(6-8) and magnetoelectric (ME) materials(9,10), have been explored for the electric-field control of magnetism. The recent discovery of two-dimensional (2D) van der Waals magnets(11,12) has opened a new door for the electrical control of magnetism at the nanometre scale through a van der Waals heterostructure device platform(13). Here we demonstrate the control of magnetism in bilayer CrI3, an antiferromagnetic (AFM) semiconductor in its ground state(12), by the application of small gate voltages in field-effect devices and the detection of magnetization using magnetic circular dichroism (MCD) microscopy. The applied electric field creates an interlayer potential difference, which results in a large linear ME effect, whose sign depends on the interlayer AFM order. We also achieve a complete and reversible electrical switching between the interlayer AFM and FM states in the vicinity of the interlayer spin-flip transition. The effect originates from the electric-field dependence of the interlayer exchange bias.