In this study, a finite volume method for the steady thermoelastic analysis of the functionally graded materials is presented. The method is validated in a benchmark case from the published paper. By incorporating the variation of material properties in the discretization process, the method is able to avoid discontinuous distributions of stresses. Two different formulations for the calculation of variable gradients are assessed. The numerical results show that the least square method achieves better performances than the Gaussian method but least square method costs slightly more iteration and computer memory under different mesh types. Then the method is applied to analyze thermoelastic problems of the functionally graded circular rotating disk under different conditions. The effects of thickness, material properties, reference temperature and temperature difference between the inner and outer surfaces on the thermoelastic performance of the disk have been studied.