Firstly, the source of potassium atoms in solid rocket engine exhaust plume and its radiation mechanism were introduced, and the spectrum of the potassium resonance doublet shape was analyzed based on the theory of atomic spectra. Secondly, the numerical simulation of the plume flow field distribution was carried out with the ideal jet model and the semi-empirical formula. The radiation spectral characteristics of potassium resonance doublet shape from rocket plume were calculated by using the C-G approximation method. Finally, the spectral characteristics of potassium resonance doublet shape signal in the wake of the plume were calculated by using the atmospheric radiative transfer model. The results demonstrate that this method can effectively simulate the fine structure of the NIR spectrum of exhaust plume. The simulation results also show that the signal energy of potassium resonance doublet spectrum can be effectively transmitted through atmosphere, which can be used as the basis for the detection and identification of exhaust plume.