Abstract The concepts of the Subspace Information Quantity(SIQ) and Function Set Information Quantity(FSIQ) are presented; Then the problem of model selection based on FSIQ are discussed explicitly, and the approximate method of model selection based on limited samples with white noise is proposed, which resolves the problem of underletting and overfitting of model selection and improves the generalization of predict model well. A new suboptimal algorithm for model selection is given, and its reliability and advantage are illustrated through concrete test.