This article deals with the analysis of combined mode non-Fourier conduction and radiation heat transfer in a concentric spherical enclosure containing a conducting-radiating medium. The finite volume method (FVM) has been employed to calculate the volumetric radiative information and also to solve the governing energy equation, which is of hyperbolic nature. The non-Fourier effect which manifests in the form of a sharp discontinuity in the temporal temperature distribution and propagates with a finite speed has been investigated. As time progress, the discontinuity in the temperature distribution decays and in the steady-state, results with and without non-Fourier effect are the same. Detailed study of the effect of various parameters such as the extinction coefficient, the scattering albedo, the conduction radiation parameter, the emissivity and the anisotropy factor has been carried out. Results of the present work have been compared with the steady-state response of the combined mode Fourier conduction-radiation problems available in literature. Results have been found to agree well. (C) 2011 Elsevier Ltd. All rights reserved.