One of the critical steps in improving accurate single neuron reconstruction from three-dimensional (3D) optical microscope images is the neuronal structure segmentation. However, they are always hard to segment due to the lack in quality. Despite a series of attempts to apply convolutional neural networks (CNNs) on this task, noise and disconnected gaps are still challenging to alleviate with the neglect of the non-local features of graph-like tubular neural structures. Hence, we present an end-to-end segmentation network by jointly considering the local appearance and the global geometry traits through graph reasoning and a skeleton-based auxiliary loss. The evaluation results on the Janelia dataset from the BigNeuron project demonstrate that our proposed method exceeds the counterpart algorithms in performance.