In the present paper, an attempt was made on calibrating mass fraction of oxygen atom which can exist in a free stream of a high enthalpy shock tunnel based on a measurement of shock stand-off distance. To correlate the free stream oxygen atom and the shock stand-off distance, a density relaxation function was derived by considering an effect of the free stream oxygen atom on density change along stagnation stream line behind the shock wave. The density relaxation function was numerically estimated with the mass fraction of oxygen atom predicted by using NENZF code and used to examine the correlation with the shock stand-off distance around the sphere model measured in the high enthalpy shock tunnel HIEST at JAXA Kakuda Space Center. The correlation between the density relaxation function considering the effect of free stream oxygen atom and the shock stand-off distance was successfully obtained, as the result the mass fraction of oxygen atom in the free stream of the HIEST could be calibrated.