Neuron　reconstruction　is　an　important　technique　in　computational　neuroscience.　There　are　many　neuron　reconstruction　algorithms,　but　few　can　generate　robust　result,　especially　when　a　3D　microscopic　image　has　low　single-to-noise　ratio.　In　this　paper　we　propose　a　neuron　reconstruction　algorithm　called　fast　marching　spanning　tree　(FMST),　which　is　based　on　minimum　spanning　tree　method　(MST)　and　can　improve　the　performance　of　MST.　The　contributions　of　the　proposed　method　are　as　follows.　Firstly,　the　Euclidean　distance　weights　of　edges　in　MST　is　improved　to　be　more　reasonable.　Secondly,　the　strategy　of　pruning　nodes　is　updated.　Thirdly,　separate　branches　can　be　merged　for　broken　neurons.　FMST　and　several　other　reconstruction　methods　were　implemented　on　the　120　confocal　images　of　single　neurons　in　the　Drosophila　brain　downloaded　from　the　flycircuit　database.　The　performance　of　FMST　is　better　than　some　existing　methods　for　some　neurons.　So　it　is　a　potentially　practicable　neuron　construction　algorithm.　But　its　performance　on　some　neurons　is　not　good　enough　and　the　proposed　method　still　needs　to　be　improved　further.