Nineteen transition metal elements have been taken into account to study the alloying effects on the relative phase stability, elastic properties and electronic structure of L1(2) Co3V compound, based on the first-principles calculations. The site preference of ternary alloying elements was primarily determined with the help of normalized transfer energy. According to the results, four groups of alloying elements were classified, namely strong/weak V site preference and strong/weak Co site preference. In view of relative phase stability, we found that the Co-V-Hf, Co-V-Ir and Co-V-Pt systems have strong potential to precipitate the stable gamma' phase, other than Co-V-Ti, Co-V-Ta systems that have been experimentally reported. The stabilizing effect of ternary alloying elements on gamma' phase has an order of Ti > Ta > Hf > Ir > Pt > Nb > Zr > Rh > Sc > W. By using stress-strain method, the elastic properties including bulk modulus, shear modulus and Young's modulus were evaluated. Significantly, the intrinsic linear relationship between elastic properties and electron density per molar volume was revealed. It is found that the shear moduli G ({110}) and G ({111}) of L1(2) Co3V compound are increased by alloying Cr, Tc, Re and Pt elements, while reduced by other transition metal elements. To understand the mechanism, we employed the charge density difference to characterize the electronic structure of some typical X-substituted L1(2) Co3V compounds. The results successfully associate the shear moduli of these compounds with the anisotropic distribution of transfer electron density.