Nanocrystalline (NC) and ultrafine-grained (UFG) CoCrCuFeNi high-entropy alloy (HEA) with grain size ranging between 59 and 386 nm was produced via powder metallurgy and heat treatment. The as-sintered HEA exhibited two face-centered cubic (FCC) phases (CoCrFeNi-rich and Cu-rich phases) and a small grain size (59 nm), whereas the alloy after heat treatment at 1000 °C exhibited a CoCuFeNi-rich phase with FCC structure and relatively larger grain size (386 nm). Moreover, the yield strength decreased from 1930 to 883 MPa, and plastic strain to failure increased by 8–32%. In terms of microstructural evolution, grain boundary strengthening coupled with lattice distortion was the dominant strengthening mechanism for NC HEAs. Furthermore, the coefficient for boundary strengthening was higher in the HEAs than in the corresponding pure elemental metals with FCC structure, possibly because of significant lattice distortion. The UFG HEAs exhibited high strength and good ductility because of the activation of dislocation.