Room-temperature skyrmions in magnetic multilayers are considered to be promising candidates for the next-generation spintronic devices. Several approaches have been developed to control skyrmions, but they either cause significant heat dissipation or require ultrahigh electric fields near the breakdown threshold. Here, we demonstrate electric-field control of skyrmions through strain-mediated magnetoelectric coupling in ferromagnetic/ferroelectric multiferroic heterostructures. We show the process of non-volatile creation of multiple skyrmions, reversible deformation and annihilation of a single skyrmion by performing magnetic force microscopy with in situ electric fields. Strain-induced changes in perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction strength are characterized experimentally. These experimental results, together with micromagnetic simulations, demonstrate that strain-mediated magnetoelectric coupling (via strain-induced changes in both the perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction is responsible for the observed electric-field control of skyrmions. Our work provides a platform to investigate electric-field control of skyrmions in multiferroic heterostructures and paves the way towards more energy-efficient skyrmion-based spintronics.