In　order　to　overcome　the　low　efficiency　of　Dijkstra　(DK)　algorithm　in　constructing　Minimal　Spanning　Trees　(MST)　for　large-scale　datasets,　this　paper　uses　Locality　Sensitive　Hashing　(LSH)　to　design　a　fast　approximate　algorithm,　namely,　LSHDK　algorithm,　to　build　MST　in　Euclidean　space.　The　LSHDK　algorithm　can　achieve　a　faster　speed　with　small　error　by　reducing　computations　in　search　of　nearest　points.　Computational　experiments　show　that　it　runs　faster　than　the　DK　algorithm　on　datasets　of　more　than　50　000　points,　while　the　resulting　approximate　MST　has　an　small　error　which　is　very　small　(0.00-0.05%)　in　low　dimension,　and　generally　between　0.1%-3.0%　in　high　dimension.