A circumferential convergent hydrodynamic finger seal is a non-contact flexible gas seal which can be used in aero-engines. According to the working performance requirements of a circumferential convergent hydrodynamic finger seal, a performance optimization model is constructed. The optimized structure of the finger seal is studied by combining a neural network with a genetic algorithm. Based on a back propagation(BP) neural network, the implicit relationship between the design parameters and objective function is established, and then the structure of a circumferential convergent hydrodynamic finger seal with better performance is obtained by the genetic algorithm. By fluid-solid interaction calculation, the dynamic responses of the circumferential convergent hydrodynamic finger seal are analyzed in the process of rotor startup and periodical radial excitation. Compared with the circumferential convergent hydrodynamic finger seal which is not optimized in the dynamic behavior, the optimized finger seal exhibited better performance characteristics. This article can provide certain theoretical foundation for designing circumferential convergent hydrodynamic finger seals with high performance.