With the first-principles density functional theory, based on ultra-soft psuedopotential method, the structure, elastic, and electronic structure properties of WC-type RexW1－xC(x=1, 0.25, 0.75, 0), Re0.5Os0.5C, and Os0.5W0.5C were studied. It was found that the shear modulus of Re0.25W0.75C is higher than that of all synthesized and theoretically predicted 5d transition metal carbides. An analysis of Mulliken population of the bond between transition metal and C atom shows that the large shear modulus of Re0.25W0.75C is mainly due to the strong covalent Re—C interaction. The low value of the density of states on the Fermi level indicates the high stability of Re0.25W0.75C. The excellent elastic property and high stability suggest that hexagonal Re0.5W0.5C can be an ultra-hard material. We hope our calculations can stimulate the experimental research to synthesize it.