This article presents a finite-volume method to calculate transient radiative transfer in a one-dimensional slab. The fully implicit scheme is used to discretize the transient term. The step and CLAM spatial differencing schemes are used in this study. The procedure is validated with available published results. The capabilities of the procedure are then examined using three additional test problems. In these test problems, one of the walls is subjected to a single-pulse collimated beam and a repeated-pulse collimated beam. The effects of the two spatial differencing schemes are discussed.