The influence of the linear birefringence on magneto-optical property measurement for optical fibers is investigated theoretically and experimentally. The evolution of polarization in fibers is simulated by the Jones matrix. To verify this theoretical model, a magneto-optical system is built to measure the input azimuth, output azimuth and ellipticity. The Faraday rotation of spun fibers with different pitches is measured. The Verdet constant increases, while the linear birefringence decreases as the pitch becomes smaller. For spun fibers with 1 mm pitch, the Verdet constant can be enhanced by about 20.7% at 660 nm, compared with that of the unspun fiber. The results indicate that smaller linear birefringence can provide more accurate Faraday rotation measurement.