Reconstruction of neural circuits from volume electron microscopy data requires the tracing of cells in their entirety, including all their neurites. Automated approaches have been developed for tracing, but their error rates are too high to generate reliable circuit diagrams without extensive human proofreading. We present flood-filling networks, a method for automated segmentation that, similar to most previous efforts, uses convolutional neural networks, but contains in addition a recurrent pathway that allows the iterative optimization and extension of individual neuronal processes. We used flood-filling networks to trace neurons in a dataset obtained by serial block-face electron microscopy of a zebra finch brain. Using our method, we achieved a mean error-free neurite path length of 1.1 mm, and we observed only four mergers in a test set with a path length of 97 mm. The performance of flood-filling networks was an order of magnitude better than that of previous approaches applied to this dataset, although with substantially increased computational costs.