To further improve the accuracy of the Virial-Peng-Long （VPL） equation of state （EOS） in describing the thermochemical relations of gaseous detonation products， and to enhance the accuracy of the VPL EOS in predicting the detonation performance of energetic materials， the abnormal inflection points in the short-range repulsive stage were corrected based on the analysis of the mathematical form of Exponential-6 （Exp-6） potential to obtain a novel exponential molecular potential： Exponential-6modified （Exp-6m） with the globally continuous and smooth potential function curve. On this basis， a high-order virial type gaseous detonation product EOS： Virial-Peng-Long modified （VPLm） EOS was established based on the theoretical values of 2-5th virial coefficients of Exp-6m potential. On one hand， the detonation Chapmann Jouguet （C-J） parameters of oxygen rich equilibrium explosives such as PETN and NG， as well as high-energy density explosives such as CL-20， were calculated using the VPLm EOS. The results show that VPLm EOS can accurately evaluate the detonation performance for explosives. The prediction deviation of detonation C-J pressure of PETN at higher densities less than 1.5%， and the prediction deviation of detonation velocity of high-density CL-20 can also be controlled within 1.6%. The calculation accuracy has been significantly improved compared to the VPL EOS. On the other hand， VPLm EOS was applied to calculate the detonation velocity of typical metal-containing primary explosive， lead azide （LA）， at different densities. The results show that the VPLm EOS had better accuracy in predicting the detonation velocity of LA than Explo5 and CHEETAH， and can more accurately evaluate the detonation velocity of LA at higher densities compared to the VPL EOS.