The principle of the polarizing atmospheric Michelson interferometer is introduced, the influence of the polarization directions of all the components on its interferential intensity and modulation depth is discussed, and the dependence of intensity and modulation depth on the deviation is calculated with the polarization direction deviating from the ideal direction. We analyze the influence on the intensity and modulation depth when the polarization directions of the polarizer, the three quarter-wave plates and the analyzer deviate from the ideal direction. The changing curves of modulation depth, wind velocity and the temperature with the deviation of the polarization direction are obtained. We also give the tolerances of all the polarization directions. These results would be helpfull for theoretical research and development of the new polarizing atmospheric Michelson interferometer. It also has scientific value and wide prospect for measuring winds in the thermosphere and for space measurement.