To reduce the drift error existing in the output signal of fiber optic gyroscopes (FOG), a mathematical model of the FOG output signal is set up; the error characteristics of the FOG output signal are analyzed, and semi-soft threshold filtering is chosen based on the comparison of hard threshold and soft threshold filtering. The semi-soft threshold wavelet package filtering method is applied in the filtering of the FOG output signal. Experiments of the stationary and dynamic FOG output signals filtered with the wavelet package analysis are carried out in a lab environment, respectively. Experiments done with the real-time measured FOG signal show that the method of semi-soft threshold wavelet package filtering reduces the mean square error from 5 (°)/h to 1 (°)/h, so it is effective in eliminating the white noises and the fractal noises existing in the FOG. The novel method proposed here is proved valid in reducing the FOG drift error, satisfying the technical demands of high precision and realtime processing.