The real-time linear measurement of the Faraday rotation angle of polarized light based on the crystal wedge is presented. Compared to the traditional methods, the measurement based on crystal wedge is not only insensitive to the light power fluctuation, but also can realize the real-time detection due to no adjustment of the optical elements during the experiments. More importantly the linear measurement can be kept for any polarization angle, and the relative accuracy reaches 8.7×10-4. The Verdet constants of the BiYIG magneto-optical film with Tb doping under various temperature are investigated by this method, and the temperature dependence is analyzed.