Our understanding of neural computations has been frustrated by the lack of detailed synaptic connection maps, or connectomes. For example, despite intensive theoretical and experimental investigations for over half a century, the neuronal implementation of local motion detection in insect visual system has never been fully mapped onto concrete neural elements. A central impediment toward unravelling the mechanism of such computations has been our incomplete knowledge of the relevant neurons and synapses. To provide a reliable foundation for computational modelling and identify targets for further functional investigations, we attempted a complete, dense reconstruction of neural circuit in the fruit fly visual system. We developed a high-throughput, semi-automated pipeline for electron microscopy (EM) reconstruction, then applied it to reconstruct a connectome module comprehensively within the medulla, a neuropil that has long resisted such attempts. Using connectomics, we identified cell types constituting a motion detection circuit, and showed that the connections onto individual motion-sensitive neurons in this circuit were consistent with their direction selectivity. Our identification of the candidate motion detection pathway was greatly aided by the comprehensiveness of our EM reconstruction. Relative to connections estimated by arbor overlap, having the precise synaptic counts allows us to unequivocally establish connections. The significance of the dense medulla connectome also goes far beyond the local motion detector, applying to many other visual computations. Our results identify cellular targets for future functional analysis, and demonstrate that connectomes can provide key insights into neuronal computations.