The principle of the polarization interference imaging spectrometer （PIIS） developed in our laboratory is described. The principle of the beam splitting of Glan-Taylor prism which is one of the key components in the PIIS is analyzed. Using the ray-tracing method, we obtain the transmittance of Glan-Taylor prism at full angle of view. By computer simulation, we analyze the influence of the incidence plane, incidence angle and thickness of air gap on transmittance, and the dependence of the transmittance on wavelength is given in the spectral range which is required by the instrument system using Sellmeier dispersion equation. The transmittance of Grand-Taylor prism is tested in experiment, and the results are in good agreement with the theoretical results, so the correctness of the theory is verified.