We report the superconducting properties of new hexagonal Nb10+2xMo35−xRu35−xRh10Pd10 high-entropy alloys (HEAs) (0 ≤ x ≤ 5). With increasing x, the superconducting transition temperature Tc shows a maximum of 6.19 K at x = 2.5, while the zero-temperature upper critical field Bc2(0) increases monotonically, reaching 8.3 T at x = 5. For all x values, the specific heat jump deviates from the Bardeen-Cooper-Schreiffer behavior. In addition, we show that Tc of these HEAs is not determined mainly by the density of states at the Fermi level and would be enhanced by lowering the valence electron concentration.Mo 22.5 Re 22.5 Ru 22.5 Rh 22.5 Ti 10 HEAs with T c values of 3.6 K and 4.7 K, respectively, though no other superconducting properties have been characterized [30]. In this context, the search for HEA superconductors with a hexagonal structure is highly desirable.