The operation of a direction-switched mode-locked fiber laser gyroscope is described, We observed a large bias in the beat: frequency output, and found that it was caused by the optical Kerr effect when the two counterpropagating pulses in the laser cavity have different optical powers. The beat frequency bias was 65 Hz per 1 mW of power difference when the scale factor of the gyroscope was 0.43 kHz/(degrees/s). We found that a small amount of backscattering in the laser cavity could result in random fluctuations in the beat frequency. It is shown that the random frequency noise can be suppressed efficiently by applying push-pull phase modulation in the laser cavity.