Based on the principle of a screw seal, a new type of seal consisting of a series of screw seals was developed and named as an axial pumping baffle seal. A theoretical analysis model was presented for such a seal which was developed to be used in nuclear coolant pumps. The feasibility of sealing high-pressure medium for such a seal had been proved. The variation of leakage rate and pressure distribution between a tooth and a sleeve with the number of seal stages and the geometrical parameters of screws was studied. The sealing mechanism was presented. The results showed that such a new seal maybe replace the first stage seal of a series mechanical seal used in a nuclear pump. When the number of screw seals is about 9, the reliability is ensured by the cooperation of the “attack” of the screw seal and the “defense” of the 180° sharp back bend.