Moiré engineering1–3 of van der Waals magnetic materials4–9 can yield new magnetic ground states via competing interactions in moiré superlattices10–13. Theory predicts a suite of interesting phenomena, including multiflavour magnetic states10, non-collinear magnetic states10–13, moiré magnon bands and magnon networks14 in twisted bilayer magnetic crystals, but so far such non-trivial magnetic ground states have not emerged experimentally. Here, by utilizing the stacking-dependent interlayer exchange interactions in two-dimensional magnetic materials15–18, we demonstrate a coexisting ferromagnetic (FM) and antiferromagnetic (AF) ground state in small-twist-angle CrI3 bilayers. The FM–AF state transitions to a collinear FM ground state above a critical twist angle of about 3°. The coexisting FM and AF domains result from a competition between the interlayer AF coupling, which emerges in the monoclinic stacking regions of the moiré superlattice, and the energy cost for forming FM–AF domain walls. Our observations are consistent with the emergence of a non-collinear magnetic ground state with FM and AF domains on the moiré length scale10–13. We further employ the doping dependence of the interlayer AF interaction to control the FM–AF state by electrically gating a bilayer sample. These experiments highlight the potential to create complex magnetic ground states in twisted bilayer magnetic crystals, and may find application in future gate-voltage-controllable high-density magnetic memory storage. © 2021, The Author(s), under exclusive licence to Springer Nature Limited.