An equiatomic CoCrFeMnNi high-entropy alloy under hydrostatic compression is investigated using in-situ angular-dispersive X-ray diffraction to explore the polymorphism in high entropy alloy systems. The metallic system is of face-centered-cubic structure at ambient condition and applied hydrostatic pressures up to 20 GPa via diamond anvil cell. The angle-resolved diffraction-intensity evolutions of multiple diffraction peaks were collected simultaneously to elucidate the phase stability examinations. The phase transformation from face-centered-cubic to hexagonal-close-packed structure was evidently observed in CoCrFeMnNi alloy accompanied by a deviatoric strain subjected to the hydrostatic compression. We found lattice-asymmetric crossover before and after the phase transformation subjected to hydrostatic compression surroundings. Deviatoric strain triggers fcc-hcp phase transformation as local heterogeneity-driven lattice distortion is significant for CoCrFeMnNi alloy.