On the basis of quantum theory,coherent anti-Stokes Raman scattering (CARS) mechanism was discussed and theoretical calculation model for Nitrogen CARS spectrum was derived.Calculations of Raman scatter section,molecule population density difference between lower and upper vibration level,rotational and vibrational fraction function and the third nonlinear susceptibility were shown.The results were proved to coincide with previous literature although some predigestion were taken.Single-pulse CARS setup which can be used in transient temperature distribution measurement were introduced.The theoretical spectral resolution can be 0.1 cm-1,the axial spatial resolution is better than 5mm and the sample repetition rate can be up to 10Hz.