Pure spin currents can be generated via thermal excitations of magnons. These magnon spin currents serve as carriers of information in insulating materials, and controlling them using electrical means may enable energy efficient information processing. Here, we demonstrate electric field control of magnon spin currents in the antiferromagnetic insulator Cr2O3. We show that the thermally driven magnon spin currents reveal a spin-flop transition in thin-film Cr2O3. Crucially, this spin-flop can be turned on or off by applying an electric field across the thickness of the film. Using this tunability, we demonstrate electric field–induced switching of the polarization of magnon spin currents by varying only a gate voltage while at a fixed magnetic field. We propose a model considering an electric field–dependent spin-flop transition, arising from a change in sublattice magnetizations via a magnetoelectric coupling. These results provide a different approach toward controlling magnon spin current in antiferromagnets.