In order to reduce the random noise of fiber optic gyroscope(FOG) and eliminate the disturbance from singular sampled signal, a robust smoothing filtering algorithm was proposed. Each sampled data of FOG were iteratively weighted by weighting function with giving outliers a low weight and allocating a relatively high weight to high quality data. Then the robustness of smoothing filter can be improved evidently. The operation speed of smoothing filtering algorithm is increased effectively by generalized cross validation(GCV) and discrete cosine transform(DCT). Simulation and practicable test results show that the proposed algorithm can restrain the interference by singular sampled signal or random noise of FOG and has better signal tracking capability.