How to construct an accurate interatomic potential function is an important and basic problem in the simulation procedure. Using first-principles method, the single atom energies in different lattice constants are calculated to achieve the ground state curves of Au and Ag. These energies are calculated in the Perdew and Zunger form of the local-density approximation ultra-soft pseudo potentials. The cut-off energies of the plane wave bases of Au and Ag are set to be 320 eV and 300 eV respectively, which are sufficient for their full converge. The Brillouin zone is all sampled with a 12×12×12 Monkhorst-Pack mesh of k points for Au and Ag. Allowable error in total energy is smaller than 1×10-6 eV per atom. The lattice cohesive energies in different lattice constants are calculated to achieve the lattice energy and atom distance curves after subtracting the value of ground state energy from each of these energy. Then the accurate inversion potential curves are obtained according to the Chen-Möbius inversion theory and self-compiled program. Based on the fitting consequences of inversion potential curves, using different potential function formulas, a double exponential potential function to fit the inversion potential is presented. This function provides the accurate formulas and parameters for the following research. Moreover, the phonon spectra and the densities of states of Au and Ag are calculated respectively by using the inversion potential data, the embedded atom method (EAM) potential theory and first principles method to verify the reliability of the inversion potential. The comparison of the results among the three methods shows that the tendencies of these curves are similar. But they still have some deviations especially in the range of high frequency. However these curves indicate that the inversion potential can reasonably reflect the interaction between atoms. Meanwhile, the inversion potential method has great advantage in calculation quantity compared with the EAM potential method. The inversion method needs less time in calculation. In addition, the thermal expansion coefficients, the elastic moduli and the Grüneisen constants of Au and Ag are also calculated based on the fitting formulas and parameters. The results agree well with the experimental data, which implies that these inversion potentials are effective and accurate.