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.