Using molecular dynamics simulations, we characterized the generation and evolution of radiation-induced point defects in the CoCrFeMnNi high-entropy alloy (HEA), to compare it with pure Ni and pure Fe. The generation of primary point defects was investigated by a cascade simulation at 773 K and the evolution of point defect clusters by a defect evolution simulation using 1 at% defect-containing samples. The numbers of residual defects after cascade and surviving defects after evolution in the CoCrFeMnNi HEA are smaller than those in pure Ni and pure Fe. The defect clusters appearing in the CoCrFeMnNi HEA after the defect evolution are unstable because of the alloy complexity. The origin of the slower radiation damage accumulation and the higher radiation damage tolerance in the CoCrFeMnNi HEA is discussed.