A spectral collocation method based on Chebyshev polynomial expansions is presented to solve three-dimensional coupled radiation-conduction heat transfer problems in absorbing，emitting and scattering media. For both the radiative transfer equation(RTE)and energy equation，the spatial domain is discretized by the Chebyshev spectral collocation method. The angular domain is discretized by the discrete ordinates method for RTE. The formulations and implementation of the spectral collocation-discrete ordinates method (SP-DOM)reveal its high efficiency. The numerical results in three-dimensional cube geometries by the SP-DOM are compared with the results in literature obtained by the finite volume method. It is found that even by the standard of the radiative heat flux and the total heat flux，which are more sensitive than temperature，the calculated results are in good agreement with the results in literature. In addition，the number of nodes used in SP-DOM is much less for the same problem. These results show that，even with a small number of nodes，the present method can provide high accuracy to solve radiative-conductive heat transfer problems in three-dimensional enclosure. The SP-DOM for three-dimensional radiative-conductive heat transfer is accurate and efficient. The predicted temperature， radiative heat flux and total heat flux distributions are presented for different parameters，such as conduction/radiation ratio，optical thickness，