Based on the theoretical analyses of the magneto-optical properties of a Bi₄Ge₃O₁₂(BGO) crystal,the Verdet constants of a BGO crystal at different wavelengths are measured employing the double frequency method. And the experimental results agree with the theoretical value. Combine the measured absorption coefficients with the relations between the Verdet constant and the light wavelengths,the magneto-optical figure of merit of the BGO crystal is presented. Additionally,the magneto-optical properties of a BGO crystal are compared with that of some magneto-optical materials usually used for optical fiber current sensor. The results show that BGO crystal is more suitable for fabricating optical fiber current sensors.