Mapping the human connectome using fibre-tracking permits the study of brain connectivity and yields new insights into neuroscience. However, reliable connectome reconstruction using diffusion magnetic resonance imaging (dMRI) data acquired by widely available clinical protocols remains challenging, thus limiting the connectome/tractography clinical applications. Here we develop fibre orientation distribution (FOD) network (FOD-Net), a deep-learning-based framework for FOD angular super-resolution. Our method enhances the angular resolution of FOD images computed from common clinical-quality dMRI data, to obtain FODs with quality comparable to those produced from advanced research scanners. Super-resolved FOD images enable superior tractography and structural connectome reconstruction from clinical protocols. The method was trained and tested with high-quality data from the Human Connectome Project (HCP) and further validated with a local clinical 3.0T scanner. Using this method, we improve the angular resolution of FOD images acquired with typical single-shell low-angular-resolution dMRI data (e.g., 32 directions, b=1000 s/mm2) to approximate the quality of FODs derived from time-consuming, multi-shell high-angular-resolution dMRI research protocols. We also demonstrate tractography improvement, removing spurious connections and bridging missing connections. We further demonstrate that connectomes reconstructed by super-resolved FOD achieve comparable results to those obtained with more advanced dMRI acquisition protocols, on both HCP and clinical 3T data. Advances in deep-learning approaches used in FOD-Net facilitate the generation of high quality tractography/connectome analysis from existing clinical MRI environments.