Benefiting　from　the　use　of　two　cover　systems,　that　is,　the　mathematical　cover　and　the　physical　cover,　the　numerical　manifold　method　(NMM)　is　capable　of　solving　both　continuous　and　discontinuous　problems　in　the　same　platform.　Presently,　the　NMM　is　further　developed　to　tackle　two-dimensional　transient　heat　conduction　problems　in　the　functionally　graded　materials　(FGMs).　Firstly,　the　governing　equation,　the　associated　boundary　conditions　and　the　initial　condition　are　presented.　Then,　the　fundamentals　of　the　NMM　are　briefly　reviewed.　Following,　the　NMM　discrete　formulations　are　derived　based　on　the　Galerkin-form　weighted　residual　method　and　then　solved　with　the　backward　difference　scheme.　Finally,　for　verification,　three　numerical　examples　with　increasing　complexity　are　tested　on　uniform　mathematical　covers　composed　of　square　mathematical　elements,　and　our　results　well　demonstrate　the　advantages　of　the　proposed　method　in　discretization　and　accuracy;　besides,　the　effects　of　material　gradient　on　the　thermal　behavior　of　FGMs　are　also　examined.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.