In this article, a newly constructed measurement system for simultaneous measurements of dielectric constant, electrical polarization, and AC-calorimetry under high pressure using a diamond anvil cell is reviewed. The system is designed to measure pressure and magnetic-field profiles of magnetoelectric properties in multiferroics. As an example, we show the results of the pressure effect on magnetoelectric properties in one of the best studied multiferroics, TbMnO₃.