The key technique of azimuth measurement system based on magneto-optical modulation is magneto-optical modulation technique, in which the accurate expression of the internal axial magnetic field of solenoid modulated by alternating current is important, however there is little study on effect of magnetic material's parameter characteristic in magnetic field. Take the magneto-optical material TGG crystal as an example, we study the influence of TGG dielectric constant change on the axial alternating magnetic field of the solenoid. Firstly, we assume that the dielectric constant of magneto-optical material in solenoid is a constant, the model of internal axial magnetic field of solenoid modulated by sine wave signal is established with the Maxwell's equations. Secondly, according to the molecular formula of TGG, the variation function of TGG dielectric constant with modulation signal frequency is acquired by VASP software. At last, the variation function is introduced into the established magnetic field model, and the effect of TGG dielectric constant on the internal axial magnetic field of solenoid modulated by sine wave signal is got. The results shows that when the modulation signal frequency rises, the TGG dielectric constant reduces, which slows the amplitude attenuation trend of internal axial magnetic field of solenoid, and advances the rapid attenuation stage in the magnetic field phase shift attenuation process, and speeds up the attenuation velocity of the rapid attenuation stage. The research method provides a reference for studying the effect of magneto-optical material on internal axial magnetic field of solenoid, and measurement precision of azimuth misalignment angle.