In　this　study,　the　moving　least　squares　based　numerical　manifold　method　(MLS-NMM)　is　presented　to　solve　three-dimensional　(3D)　transient　heat　conduction　problems　of　functionally　graded　materials　(FGMs),　where　the　increment　dimensional　precise　integration　method　(IPIM)　is　applied　to　integrate　the　ordinary　differential　equations　derived　from　the　semi-discrete　form.　In　the　3D　MLS-NMM,　the　influence　domains　of　the　MLS-nodes　are　taken　as　the　mathematical　patches　which　are　used　to　construct　the　mathematical　cover　(MC),　and　the　shape　functions　of　the　MLS-nodes　are　employed　as　the　weight　functions　subordinate　to　the　MC.　MLS-NMM　is　utilized　for　spatial　discretization　of　the　weak　form　of　the　problem.　The　IPIM　overcomes　the　shortcomings　of　traditional　backward　difference　scheme　dependent　on　the　time　step　and　greatly　improves　the　computing　efficiency.　Meanwhile,　a　mass　lumping　technique　is　proposed　for　the　3D　MLS-NMM.　Furthermore,　a　number　of　numerical　experiments　on　transient　thermal　conduction　are　conducted,　suggesting　that　the　3D　MLS-NMM　based　on　IPIM　and　the　proposed　mass　lumping　has　excellent　accuracy,　absolutely　stable　and　high　computing　efficiency.　©　2023