In　this　study,　we　aim　to　numerically　solve　two-dimensional　nonlinear　transient　heat　conduction　problems　of　functionally　gradient　materials　(FGMs),　where　the　governing　equation　is　a　quasilinear　partial　differential　equation　of　second　order.　For　this　purpose,　the　weak　form　of　the　initial　boundary　value　problem　is　first　estab-lished.　Then　influence　domains　of　nodes　in　the　moving　least　squares　(MLS)　instead　of　finite　elements　are　used　as　the　mathematical　patches　to　construct　the　mathematical　cover　of　the　numerical　manifold　method　(NMM);　while　the　shape　functions　of　MLS-nodes　as　the　weight　functions　subordinate　to　the　mathematical　cover,　leading　to　the　moving　least　squares　based　numerical　manifold　method　(MLS-NMM).　With　the　weak　form,　the　spatial　dis-cretization　is　carried　out　using　MLS-NMM,　whereas　temporal　discretization　follows　the　Euler　backward　differ-ence.　Finally,　a　series　of　numerical　experiments　are　conducted　concerning　transient　heat　conduction　problems　of　FGMs　with　heat　source　and　heat　convection,　suggesting　that　the　proposed　MLS-NMM　enjoys　advantages　of　both　MLS　and　NMM　in　solving　nonlinear　transient　heat　conduction　of　FGMs.