Owing to the structure of the gear-claw rotor, working chambers of claw pumps are divided into small multi-chambers by a pair of intermeshing claw rotors in the mixing process, and the transient flow in multi-chambers is complicated, which results in the increase of the pump consumption. Hence, it is necessary to study the transient flow and working process of gear-claw hydrogen circulating pumps to optimize the pump performance. In this study, the meshing model of a high-order curve and its conjugate curve was proposed, and the profile composition of the gear-claw rotor was introduced. The influence of the radius ratio of claw addendum arc on the performance including relative carryover, built-in volume ratio and volume utilization was analyzed. The flow field of gear-claw hydrogen circulating pump including pressure and velocity field was analyzed by using numerical simulations. Furthermore, the p-V diagram of pumps was obtained. It is found that the gas in the compression chamber is mixed with the gas in the carryover, and the initial pressure in the compression chamber is 130.78kPa, which increases by 29.07% compared to the original initial pressure in the compression chamber. Therefore, an overcompression phenomenon at the end of the compression process (at the beginning of the discharge process) occurs.