The purpose of this study is to clarify the possibility of designing a small rotational fuel-shuffling breed-and-burn fast reactor (RFBB) with nitride fuel and sodium coolant based on neutronic and heat removal analyses. In these reactor analyses, uranium nitride fuel with a helium bond and sodium coolant was applied to the RFBB, whose thermal power is 450 MW. The structural and cladding materials are oxide dispersion-strengthened ferritic steel. Calculation results showed that the core with rotational fuel shuffling achieved an equilibrium state at criticality near unity, and the average discharge burnup of discharged fuel was 187 MWd/kg heavy metal. In this equilibrium state, reactor characteristics, such as neutron flux and the power profile, were almost stable, and the maximum displacements-per-atom value was slightly higher than 650. A steady-state heat removal analysis was performed for the hottest channel in the core, revealing that the fuel temperature was lower than the operational limit temperature and that the cladding temperature was lower than its melting temperature. However, it was slightly higher than the suggested value of 600°C for retaining nitride fuel integrity for high burnup. It was shown that the core radius could be smaller than that of the metal-fueled core of the previous study.