Combined　the　moving　least　squares(MLS)　based　on　the　approximation　of　nodes　with　numerical　manifold　method(NMM),　the　meshfree-numerical　manifold　method　is　developed,　abbreviated　as　MLS-NMM.　MLS-NMM　owns　lower　mesh-dependency　and　higher　calculate　precision　than　NMM,　and　naturally　solves　the　continuous　and　non-continuous　problems　in　a　unified　way.　To　increase　the　adaptability　of　MLS-NMM　about　analyzing　the　linear　elastic　fracture　problems,　a　new　MLS-NMM　is　proposed.　It　makes　the　mathematical　patches　containing　the　same　crack　tip　integrate　into　a　complex　patch,　in　which　the　finite　items　of　Williams＇　displacement　series　are　defined　as　the　local　approximation　in　ordering　to　reproduce　the　displacement　field　of　the　crack　tip.　And　the　method　of　quadtree＇s　local　refinement　is　adopted　to　enhance　the　calculate　precision　in　the　vicinity　of　the　crack　tip.　This　method　can　directly　acquire　the　stress　intensity　factors(SIFs)　using　the　relationship　between　SIFs　and　items　of　Williams＇　displacement　series,　avoiding　post-processing　solution　such　as　the　interaction　integral　method.　In　this　paper,　the　maximum　circumferential　stress　criterion　is　applied　to　decide　the　direction　of　crack　propagation.　At　last,　two　examples　of　SIF　and　two　examples　of　crack　propagation　are　simulated,　the　results　reveal　that　the　proposed　method　can　effectively　deal　with　the　linear　elastic　fracture　problems,　and　simultaneously　suggest　that　2　layer　local　refinement　and　9　items　of　Williams＇　displacement　series　should　be　used.　©　2020,　Science　Press.　All　right　reserved.