We report electric-field control of magnetism of (Co/Pt)₃ multilayers involving perpendicular magnetic anisotropy with different Co-layer thicknesses grown on Pb(Mg,Nb)O₃-PbTiO₃ (PMN-PT) FE substrates. For the first time, electric-field control of the interface magnetic anisotropy, which results in the spin reorientation transition, was demonstrated. The electric-field-induced changes of the bulk and interface magnetic anisotropies can be understood by considering the strain-induced change of magnetoelastic energy and weakening of Pt 5d-Co 3d hybridization, respectively. We also demonstrate the role of competition between the applied magnetic field and the electric field in determining the magnetization of the sample with the coexistence phase. Our results demonstrate electric-field control of magnetism by harnessing the strain-mediated coupling in multiferroic heterostructures with perpendicular magnetic anisotropy and are helpful for electric-field modulations of Dzyaloshinskii-Moriya interaction and Rashba effect at interfaces to engineer new functionalities.