Abstract: A manifold extended t-process regression (meTPR) model is developed to fit functional data with a complicated input space. A manifold method is used to transform covariate data from input space into a feature space, and then an extended t-process regression is used to map feature from feature space into observation space. An estimation procedure is constructed to estimate parameters in the model. Numerical studies are investigated with both synthetic data and real data, and results show that the proposed meTPR model performs well.