In order to improve the thermal stability and mechanical properties of W-free light-weight Co–V–Ta-based superalloys, the effects of alloying elements including Sc, Ti, Cr, Mn, Fe, Ni, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Hf, W, Re, Os, Ir, and Pt on γ′-Co3(V, Ta) stability and elastic properties were studied. The results from the reaction energy indicate that Sc, Ti, Y, Zr, Nb, Mo, Hf, and W tend to occupy the V site, whereas Cr, Mn, Fe, Ni, Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt prefer to occupy the Co site. It was found that Sc, Ti, Y, Zr, Fe, and Mn stabilize the γ′-Co3(V, Ta) phase by raising the phase-transfer energy. The addition of Mo and W increases the bulk modulus, shear modulus, and Young’s modulus. According to Pugh’s classical criterion, the γ′-Co3(V, Ta) phase is an intrinsically brittle material, and the addition of elements such as Tc and Re significantly enhances the ductility. At finite temperature, the doping of Sc, Ti, Mn, Fe, and Hf enhances the relative stability of the γ′-Co3(V, Ta) phase in the whole temperature range from 0 to 1200 K and are candidates for improving the stability of the γ′-Co3(V, Ta) phase.