In order to solve the transient heat conduction problems in three-dimensional(3D) axisymmetric continuously nonhomogeneous functionally graded materials(FGMs) more effectively, a novel numerical method based on the meshless natural element method is proposed. Axial symmetry of geometry and boundary conditions helps to transform the 3D axisymmetric problem into a two-dimensional(2D) prolem. In order to simplify the imposition of the essential boundary conditions, the natural neighbour interpolation is adopted to discretize the temperature field within the cross section. The variations of functionally graded material properties are simulated by employing proper material parameters at Gauss points. The spatially discretized heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. The present method not only broadens the application scope of the natural element method, but also will be generally available to transient heat conduction analyses of 3D axisymmetric solids.