The structural changes induced in a CoCrCuFeNi multicomponent nano-crystalline high-entropy alloy (HEA) under fast electron irradiation were investigated by in-situ transmission electron microscopy (TEM) using a high voltage electron microscope (HVEM). A fine-grained face centered cubic (fcc) single phase was obtained in the sputtered specimens. The fcc solid solution showed high phase stability against irradiation over a wide temperature range from 298 to 773 K, and remained as the main constituent phase even when the samples were irradiated up to 40 displacement per atom (dpa). Moreover, the irradiation did not seem to induce grain coarsening. This is the first report on the irradiation damage in 5-component HEA under MeV electron irradiation.