A finite-volume solution procedure for radiative heat transfer in a three-dimensional nonorthogonal enclosure containing participating medium is proposed with geometric relations commonly adopted in computational fluid dynamics. A general discretization equation is formulated by using the directional weight and the step scheme for spatial differencing. The present approach is validated through comparison with the problems of hexahedral enclosure, annular sector, and three-dimensional combustion chamber, in which the solution accuracy as wed as computation efficiency required have been examined for various cases. All of the results presented here support its accuracy as well as moderate efficiency in computation time in the nonorthogonal three-dimensional radiation calculation. Finally, the present method is applied to a kidney-shaped combustion chamber as a three-dimensional test case.