The drift of a fiber optic gyroscope (FOG) has a significant impact on the precision of an inertial navigation system (INS). In order to predict the FOG drift more efficiently, we have developed a method of reducing the drift using a hybrid-forecasting model. In the proposed model, the systematic and random parts of the FOG drift data are decomposed using the empirical mode decomposition (EMD) model. Then the systematic part is predicted by employing the adaptive residual grey model [ARGM (1, 1)], and the random part is predicted by the improved autoregressive moving-average (IARMA) model. The final prediction results are the superimposition of the respective prediction using the EMD reconstruction model. The experimental results show that the gyroscope drift can be forecast precisely and can provide a basis for gyroscope performance analysis and fault prediction. At the same time, it can be concluded that the hybrid modeling has a higher forecasting precision than the single forecasting method.