In order to improve the measurement precision of the traditional azimuth measurement system theoretically, as the new modulation signal, triangle wave is introduced into the system, and the method of measuring azimuth based on triangle wave magneto-optical modulation is present. In the new method, the model of modulation signal is present, and the model of the signal from modulator is present too according to the Faraday effect and Malous law. The signal from modulator is analyzed, its extremums is detected, the relationship between azimuth and extremums is present, and then the model of measuring azimuth is established. The measurement precision and scale of the new method is analyzed, simulation results show that the measurement precision of the new method is higher than the traditional one, and their measurement scale is same, it provides a new scheme to measuring azimuth in higher-precision.