Small long-life reactor is required for some local areas. CANDLE small long-life fast reactor which does not require control rods, mining,enrichment and reprocessing plants can satisfy this demand. In a CANDLE reactor, the shapes of neutron flux, nuclide number densities andpower density distributions remain constant and only shift in axial direction.The core with 1.0 m radius, 2.0 m length can realize CANDLE burn-up with nitride (enriched N-15) natural uranium as fresh fuel. LeadeBismuth is used as coolant.From steady state analysis, we obtained the burn-up velocity, output power distribution, core temperature distribution, etc. The burn-up velocityis less than 1.0 cm/year that enables a long-life design easily. The core averaged discharged fuel burn-up is about 40%.