Current fMRI data modeling techniques such as Independent Component Analysis (ICA) and Sparse Coding methods can effectively reconstruct dozens or hundreds of concurrent interacting functional brain networks simultaneously from the whole brain fMRI signals. However, such reconstructed networks have no correspondences across different subjects. Thus, automatic, effective and accurate classification and recognition of these large numbers of fMRI-derived functional brain networks are very important for subsequent steps of functional brain analysis in cognitive and clinical neuroscience applications. However, this task is still a challenging and open problem due to the tremendous variability of various types of functional brain networks and the presence of various sources of noises. In recognition of the fact that convolutional neural networks (CNN) has superior capability of representing spatial patterns with huge variability and dealing with large noises, in this paper, we design, apply and evaluate a deep 3D CNN framework for automatic, effective and accurate classification and recognition of large number of functional brain networks reconstructed by sparse representation of whole-brain fMRI signals. Our extensive experimental results based on the Human Connectome Project (HCP) fMRI data showed that the proposed deep 3D CNN can effectively and robustly perform functional networks classification and recognition tasks, while maintaining a high tolerance for mistakenly labelled training instances. Our work provides a new deep learning approach for modeling functional connectomes based on fMRI data. We envision that 3D CNN model will significantly advance current state-of-the-art fMRI data modeling approaches and pave the way for adopting fMRI into clinical management of brain disorders in the future.