Applying electric field to control magnetic properties is a very efficient way for spintronics devices. However, the control of magnetic characteristics by electric fields is not straightforward, due to the time-reversal symmetry of magnetism versus spatial inversion symmetry of electricity. Such fundamental difficulty makes it challenging to modify the topology of magnetic skyrmionic states with electric field. Here, we propose a novel mechanism that realizes the electric-field ($E$) switching of magnetic topological charge ($Q$) in a controllable and reversible fashion, through the mediation of electric polarization ($P$) and Dzyaloshinskii-Moriya interaction ($D$). Such a mechanism is coined here EPDQ. Its validity is demonstrated in a multiferroic ${\mathrm{VOI}}_{2}$ monolayer, which is predicted to host magnetic bimerons. The change in magnetic anisotropy is found to play a crucial role in realizing the EPDQ process and its microscopic origin is discussed. Our study thus provides a new approach toward the highly desired electric-field control of magnetism.