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In order to solve the high energy level is very difficult available, the product approximation model is used in this paper. By the product approximation construction model, the total internal partition functions are calculated at the temperatures from 70 to 6000K for 14N16O2. There into, the rotational partition sums Qrot adopt the WATSON rigid rotator model, which take into account centrifugal distortion corrections. The vibrational partition sums Qvib use the harmonic oscillator approximation model. The results show that the calculated values of total internal partition functions are consistent with those offered by HITRAN database from 70K to 3000K, and the errors shows linear correlation approximately. By fitting the errors, the total internal partition functions at high temperature range of 3000K to 6000K were corrected. The corrected total internal partition functions are fitted by a four-order polynomial expression in T, and the coefficients are gained at high temperature. This provides a rapid and accurate calculation of the total internal partition functions at the temperature from 3000K to 6000K.