A new meshless method, named collocation method with barycentric Lagrange interpolation (BLIC), is presented for analyzing steady-state heat conduction in two-dimensional functionally graded materials(FGMs). Two-variable barycentric Lagrange interpolation function and its partial derivatives at Chebyshev nodes are derived. Then, based on a collocation method, it is directly introduced into controlling equations and boundary conditions of GEMs to obtain a linear discretijed equation. The method is a truly meshless method and takes advantages of both barycentric Lagrange interpolation and collocation method such as low computational cost, stable, accurate and easy to numerical implementation. Temperature fields of exponential, quadratic and trigonometrical FGMs models are simulated. It shows that the method is accurate and efficient, and is not sensitive to the change of material gradient parameters. It can be extended to solve transient heat conduction and thermal stress analysis of FGMs.