High-entropy alloys (HEAs) with an atomic arrangement of a hexagonal close-packed (hcp) structure were found in YGdTbDyLu and GdTbDyTmLu alloys as a nearly single hcp phase. The equi-atomic alloy design for HEAs assisted by binary phase diagrams started with selecting constituent elements with the hcp structure at room temperature by permitting allotropic transformation at a high temperature. The binary phase diagrams comprising the elements thus selected were carefully examined for the characteristics of miscibility in both liquid and solid phases as well as in both solids due to allotropic transformation. The miscibility in interest was considerably narrow enough to prevent segregation from taking place during casting around the equi-atomic composition. The alloy design eventually gave candidates of quinary equi-atomic alloys comprising heavy lanthanides principally. The XRD analysis revealed that YGdTbDyLu and GdTbDyTmLu alloys thus designed are formed into the hcp structure in a nearly single phase. It was found that these YGdTbDyLu and GdTbDyTmLu HEAs with an hcp structure have delta parameter (δ) values of 1.4 and 1.6, respectively, and mixing enthalpy (ΔHmix) = 0 kJ/mol for both alloys. These alloys were consistently plotted in zone S for disordered HEAs in a δ-ΔHmix diagram reported by Zhang et al. (Adv Eng Mater 10:534, 2008). The value of valence electron concentration of the alloys was evaluated to be 3 as the first report for HEAs with an hcp structure. The finding of HEAs with the hcp structure is significant in that HEAs have been extended to covering all three simple metallic crystalline structures ultimately followed by the body- and face-centered cubic (bcc and fcc) phases and to all four simple solid solutions that contain the glassy phase from high-entropy bulk metallic glasses.