Aiming at the thermodynamic state description of high temperature and high pressure gases under detonation circumstance, a contrast state type virial equation of state(EOS) named as VHL(Viral-Han-Long) based on Lennard-Jones(LJ) potential function is presented in this study. Based on the VHL EOS and optimized LJ potential parameters, the thermodynamic relations of pressure, volume and temperature(pVT)of detonation products component carbon dioxide (CO₂) were calculated and compared with the calculated results by VLW EOS. Results show that the average absolute deviation(AAD) of the volume is about 0.971% and the maximum error is 4.04%, the average absolute deviation(AAD) of the volume obtained by VLW EOS is about 20.2% and the maximum error is 87.149%. In describing the thermodynamic state of CO₂ at high temperature and high pressure, VLW EOS has an obvious dependence on temperature. At the detonation environment temperature, the calculated deviation of the volume decreases with the rise of temperature. Compared with VLW EOS, VHL EOS can better describe the pVT thermodynamic relations of high temperature and high pressure CO₂ gas under detonation environment.