Based on the available data of specific heat Cv at constant volume and the Grüeisen parameter γ of both lattice and electron contributions, we present a consistent method for simultaneously calculating the effective or synthesized Grüeisen parameter along Hugoniot, γeH, covering solid, mixed, and liquid states, and the melting temperature Tm for ε-iron.The rationality validation for this method is confirmed as compared with the experimental data, including the measured Tm and Hugoniot bulk sound velocities Cb.The calculated γeH and Tm for ε-iron at the Earths inner-core boundary (330GPa) are 1.58 and 5930K, respectively, which are close to the values of 1.53 and 6050K given by Anderson [J.Phys.Chem.Solids 64 (2003) 2125].This method for determination of γeH could be, in principle, also applicable to any thermodynamic state calculations, e.g., along isothermal and isentropic paths, other than the Hugoniot locus.