Neuron reconstruction is an important technique in computational neuroscience. Although there are many reconstruction algorithms, few can generate robust results. In this paper, we propose a reconstruction algorithm called fast marching spanning tree (FMST). FMST is based on a minimum spanning tree method (MST) and improve its performance in two aspects: faster implementation and no loss of small branches. The contributions of the proposed method are as follows. Firstly, the Euclidean distance weight of edges in MST is improved to be a more reasonable value, which is related to the probability of the existence of an edge. Secondly, a strategy of pruning nodes is presented, which is based on the radius of a node's inscribed ball. Thirdly, separate branches of broken neuron reconstructions can be merged into a single tree. FMST and many other state of the art reconstruction methods were implemented on two datasets: 120 Drosophila neurons and 163 neurons with gold standard reconstructions. Qualitative and quantitative analysis on experimental results demonstrates that the performance of FMST is good compared with many existing methods. Especially, on the 91 fruitfly neurons with gold standard and evaluated by five metrics, FMST is one of two methods with best performance among all 27 state of the art reconstruction methods. FMST is a good and practicable neuron reconstruction algorithm, and can be implemented in Vaa3D platform as a neuron tracing plugin.