Jahn–Teller distortions are often observed in CuII-containing complex oxides resulting in remarkable changes of physical properties. Tuning the Jahn–Teller distortions with pressure has attracted considerable interest but is less studied in CuII-containing high-entropy oxides (HEOs). We found that pressure can suppress the structural distortions originating from the Jahn–Teller effect of CuO6 octahedra in the rock salt-type (Mg0.2Ni0.2Co0.2Zn0.2Cu0.2)O HEO and significantly modify its electronic properties. Synchrotron x-ray diffraction shows that the structural distortions arising from the Jahn–Teller effect of CuO6 octahedra are progressively suppressed, and the distorted structure evolves into a nearly ideal form under compression. Alternating current impedance and ultraviolet-visible absorption measurements reveal a dramatic resistance drop by more than three orders of magnitude and an obvious bandgap decrease in ∼0.1 eV, respectively, accompanied by the pressure-induced suppression of structural distortions. Our study presents a promising route for tuning the structural distortions and the electronic structures of CuII-containing HEOs for optimizing materials functionalities.