As the quality of filter in a solar magnetic field telescope with a birefringent filter directly affects the transmission band and the measurement of solar magnetic field,this paper researches the error factors that causes the shift of transmission band. By using computer program, the ray trace is simulated completely,and the variation of transmission band with different errors is obtained accurately. Analysis results provide the primary error terms that cause the band shift, band broadening, and the changes of maximum and minimum. Among these errors, the incident angle, optical axis tilt error of crystal, thickness error of crystal, and the optical axis azimuth error of quarter-wave plate affect the band shift.Moreover, the optical axis azimuth error of crystal affects the band broadening,and the transmission band will be broadened by 0.078% when the error is 2°. The optical axis azimuth error of a half-wave plate in a the wide field effects evidently on the maximum,and the maximum decrease by 0.487% when the error is 2°.Furthermore, the optical axis azimuth error of crystal, retardance error of half-wave plate in the wide field, and the optical axis azimuth error of quarter-wave plate have different effects on the minimum.