In　this　study,　the　moving　least　squares　based　numerical　manifold　method　(MLS-NMM)　is　firstly　applied　to　discretize　three-dimensional　(3D)　steady　heat　conduction　problems　of　functionally　graded　materials　(FGMs).　In　the　3D　MLS-NMM,　the　influence　domains　of　nodes　in　the　moving　least　squares　(MLS)　are　used　as　the　mathematical　patches　to　construct　the　mathematical　cover　(MC);　while　the　shape　functions　of　MLS-nodes　as　the　weight　functions　subordinate　to　the　MC.　Compared　with　the　traditional　NMM　using　finite　elements　to　form　the　MC,　the　cutting　operations　in　generating　the　physical　cover　are　unnecessary　and　the　computation　complexity　is　decreased　significantly.　Based　on　the　Galerkin　method,　the　discrete　form　of　3D　heat　conduction　is　derived.　Finally,　a　series　of　numerical　experiments　concerning　steady　heat　conduction　problems　are　performed,　suggesting　that　the　proposed　MLS-NMM　enjoys　advantages　of　both　MLS　and　NMM　in　solving　steady　heat　conduction.　©　2023　Elsevier　Ltd