A conceptual design for a 50MWe sodium cooled, U-Pu-Zr metallic fuelled, fast reactor core, which aims at a core lifetime of 30 years, has been performed [1]. As for the compensation for a large burn-up reactivity through 30 years, an axially movable reflector, which is located around the core, carries the major part of it and a burnable poison does the rest. This concept has achieved not only a long core lifetime but also a high discharged burn-up. On this study, a conceptual design for a small fast reactor loading U-Zr metallic fuelled core instead of U-Pu-Zr fuelled core has been conducted, based on the original core arrangement of 4S reactor [2]. Within the range of this study including safety requirements, adopting the burnable poison would be effective to construct a core concept that achieves both a long lifetime and a high discharged burn-up.