The　meshless　numerical　manifold　method　(MNMM)　inherits　two　covers　of　the　numerical　manifold　method.　A　mathematical　cover　is　composed　of　nodes＇　influence　domains　and　a　physical　cover　consists　of　physical　patches,　which　are　produced　through　cutting　mathematical　cover　by　physical　boundaries.　Because　two　covers　are　adopted,　MNMM　can　naturally　and　uniquely　solve　both　the　continuous　and　discontinuous　problems　under　Galerkin＇s　variational　framework.　However,　Galerkin＇s　meshless　method　needs　background　integration　grids　to　realize　solving,　which　often　does　not　match　the　nodes＇　influence　domains,　so　the　accuracy　of　numerical　integration　is　reduced.　Consider　that　MNMM　allows　even　distribution　of　nodes　and　the　physical　cover　contains　the　characteristics　of　the　boundary　and　nodes＇　influence　domains,　the　study　presents　a　new　numerical　integration　strategy　to　ensure　that　the　background　integration　grids　match　the　nodes＇　influence　domains.　The　method　can　be　applied　to　continuous　and　discontinuous　problems,　and　is　proved　to　be　equivalent　to　the　influence　domain　integration.　At　the　same　time,　a　reasonable　arrangement　of　mathematical　nodes　is　made　to　assure　the　background　integration　grid　that　it　is　accordant　and　straightforward.　In　this　way,　the　number　of　physical　patches　of　each　integral　point　is　the　same,　which　improves　the　accuracy　of　interpolation　calculation.　The　effectiveness　of　the　proposed　method　is　verified　by　numerical　examples　of　both　continuous　and　discontinuous　problems.