To cope with the energy crisis and environmental challenges, wind power hydrogen generation system has become an important direction for new energy utilization with its clean and efficient features. In this paper, a scheduling control method based on improved genetic algorithm is proposed for off-grid wind power hydrogen generation system under battery and electrolyzer degradation conditions. A system model considering the degradation characteristics of batteries and electrolysers is constructed, a rule-based control strategy is adopted to coordinate the energy interaction between source-load-storage, and a nonlinear adaptive cross-variance probability mechanism is designed to achieve efficient optimization of the system configuration. The results show that the spatial evaluation index SP and generation distance GD of the improved genetic algorithm on the ZDT3 test function are 0.0045 and 0.0012, respectively, which are significantly better than the traditional genetic algorithm. An arithmetic analysis based on wind speed data in a sea area shows that the optimized system is able to achieve a levelized hydrogen cost of 22.84 Yuan/kg and a 4.53% probability of missing hydrogen supply. The sensitivity analysis found that the system LHSP remained below 18% and the LCOH ranged from 18 to 34 yuan over the parameter variation interval of [-45%,45%], indicating that the system has strong hydrogen supply capability and investment robustness. The study provides an effective method for the efficient operation and economic evaluation of off-grid wind power hydrogen production system, which is of reference value for promoting the integration of renewable energy and hydrogen energy.