In recent years, a functional mixed model (FMM) has attracted considerable attention in longitudinal data analysis, because of its flexibility. The FMM consists of a fixed effect or a population mean function and some subject-specific functional random effects. In this paper, we introduce the FMM constructed by using a basis expansion technique and a Gaussian process regression, and consider the model evaluation and selection problem for the estimated model. When estimating the unknown parameters included in the FMM by the maximum penalized marginal likelihood method, the FMM is extremely sensitive to the choice of tuning parameters. In order to appropriately select them, we derive two model selection criteria for the FMM based on the perspective of information or Bayesian theories by using a marginalization approach. We conduct Monte Carlo simulations to investigate the effectiveness of our proposed modeling procedures. The proposed modeling procedures for the FMM are applied to the analysis of a longitudinal gene expression data.