Considering that traditional methods can't make accurate predictions to MEMS gyroscope's random drift, we put forward an interval prediction method by using the Support Vector Machine(SVM) model based on fuzzy information granulation. First, the original data is preprocessed with fuzzy information granulation algorithm to divide the sample space into multiple subspaces for reducing the sample size and decreasing the time complexity. Then, the scalar gyroscope random drift time series is embedded to an assistant phase space by the technology of phase construction and the data is normalized. SVM is used to conduct regression analysis, and the optimal regulation parameters of the model are obtained by using cross validation algorithm, thus to avoid over fitting and under fitting phenomenon. At last, we predict the random drifts with the trained model. The results show that the model can effectively predict variation trend and interval. Therefore, the model has a good prospect in engineering.