La2CoMnO6 (LcmO)-ZnO nanocomposite thin films grown on SrTiO3 and Nb-SrTiO3 (001) are investigated. The films grow in the form of self-assembled epitaxial vertically aligned structures. We show that, at 120 K, an electric field applied across the nanocomposite reversibly alters magnetic properties of LcmO. The effect is consistent with charge-mediated coupling between magnetism and an electric field that can be induced by changes in ion valences.