In this study, we have estimated Pressure-Volume-Temperature (P-V-T) relationship and excess specific heat atconstant pressure of hydrogen-oxygen mixture gas using an ab-initio intermolecular potential function and validated aclassical mixing rule for the mixture gas, which is one of the most representative mixing rules. As a result, the classicalmixing rule showed a good agreement with our calculation result at least for the Pressure-Volume-Temperature (P-V-T)relationship while it was poor for the excess specific heat.