Liquid sodium is mainly used as a cooling fluid in the liquid metal fast breeder reactor (LMFBR), whose heat transfer, whether convective heat transfer or boiling heat transfer, is different from that of water. So it is important for both normal and accidental operations of LMFBR to perform experimental research on heat transfer to liquid sodium and its boiling heat transfer. This study deals with heat transfer with high temperature (300-700℃) and low Pe number (20～70) and heat transfer with low temperature (250～270℃) and high Pe number (125～860), and its incipient boiling wall superheat in an annulus. Research on heat transfer involves theoretical research and experiments on heat transfer to liquid sodium. It also focuses on the theoretical analysis and experimental research on its incipient boiling wall superheat at positive pressure in an annulus. Semiempirical correlations were obtained and they were well coincident with the experimental data.