The electric field effect on the magnetism in a MgO/Pd/Co system, in which a magnetic moment is induced in the Pd layer owing to the ferromagnetic proximity effect, has been investigated using various experimental methods. An electric field was applied to the surface of the Pd layer through a solid-state HfO2/MgO dielectric bilayer by applying a gate voltage with a back-gating configuration. Changes in the magnetic properties of the system as a result of gate voltage application were detected using magnetization and polar-Kerr effect measurements as well as X-ray absorption and X-ray magnetic circular dichroism (XMCD) spectroscopies. A systematic change in the magnetic moment of the system by the application of a gate voltage is observed. The magnetic hysteresis loops obtained by the polar-Kerr effect measurement and the element-specific XMCD signal at the Co L3-edge clearly show a reproducible change in the coercivity that is dependent on the gate voltage.