<p>This paper presents a meshless numerical approach to the heat conduction analysis of multi-directional functionally graded materials (FGMs) with non-uniform boundary conditions (BCs) and heat sources. A novel three dimensional (3D) Chebyshev spectral approximation scheme is proposed to discretize and approximate the spatially varying material properties and boundary conditions. Without meshing, a simple and unified discrete governing equation is derived for 2D and 3D transient heat conduction problems of multi-directional FGMs. A series of numerical experiments are performed to validate the convergence and accuracy of the method, considering various FGMs, non-uniform BCs and heat sources. The results converge rapidly and agree well with analytical solutions and finite element simulation results. The advantage of this method is that it can handle non-homogeneous material with non-uniform BCs and heat loads without meshing, and is independent of the laws of material gradients and variation of BCs and heat sources, and has a consistent form in 2D and 3D problems.</p>