Polymorphism, which describes the occurrence of different lattice structures in a crystalline material, is a critical phenomenon in materials science and condensed matter physics. Recently, configuration disorder was compositionally engineered into single lattices, leading to the discovery of high-entropy alloys and high-entropy oxides. For these novel entropy-stabilized forms of crystalline matter with extremely high structural stability, is polymorphism still possible? Here by employing in situ high-pressure synchrotron radiation X-ray diffraction, we reveal a polymorphic transition from face-centred-cubic (fcc) structure to hexagonal-close-packing (hcp) structure in the prototype CoCrFeMnNi high-entropy alloy. The transition is irreversible, and our in situ high-temperature synchrotron radiation X-ray diffraction experiments at different pressures of the retained hcp high-entropy alloy reveal that the fcc phase is a stable polymorph at high temperatures, while the hcp structure is more thermodynamically favourable at lower temperatures. As pressure is increased, the critical temperature for the hcp-to-fcc transformation also rises.