Abstract: As a powerful tool of data modeling and analysis, the mixture of Gaussian processes (MGP) is widely used in the fields of time series regression and prediction. In the conventional MGP models, the mean function of each GP model is assumed to be zero, but this assumption is not reasonable for many practical applications. In order to get rid of this limitation, Gaussian process functional regression (GPFR) is constructed to make the mean function learnable so that the mixture of GPRs (MGPFR) is more flexible for time series modeling. In the same way, we meet the model selection problem when using the MGPFR model. In order to solve this problem, we generalize the SBC and propose the model selection and dynamic model selection algorithms to the case of the MGPFR models. It is demonstrated by the experiments that the model selection and dynamic model selection algorithms for the MGPFR models perform well on both model selection and prediction, and can be successfully applied to curve classification.