Most part of an amount of uranium contained in the spent nuclear fuel is removed by making fluorine or a fluorochemical act on the spent nuclear fuel to convert the uranium into UF.sub.6, and the uranium is purified through a simple method of distilling the UF.sub.6 together with a absorbent. After removing the most part of the amount of uranium, the remaining nuclear fuel material is dissolved and then transferred to an extraction process to recover plutonium. By doing so, a small sized dry process can be employed as a uranium purification process. Since the nuclear fuel material is dissolved and extracted after removing most part of an amount of uranium, a volume of processing solution can be reduced and the machine installation scale can be made small. Accordingly, the reprocessing facility can be extremely downsized.