The development of off-grid wind power to hydrogen systems is crucial for promoting renewable energy, reducing dependence on fossil fuels, and achieving sustainable energy development. However, the volatility of wind power can lead to problems such as shortened service life of batteries and electrolyzers. This study proposes an optimized scheduling strategy for off-grid wind power hydrogen generation systems, considering the degradation of batteries and electrolyzers, with a focus on the impact of battery state of charge (SOC) overrun and electrolyzer overload on system operation. A voltage degradation model for electrolyzers was established by analyzing different operating conditions, aiming to improve utilization capacity and reduce degradation costs. Additionally, a degradation model for energy storage batteries was developed, considering factors such as cycle depth, cycle number, and SOC overrun, to optimize charging and discharging operations, extend battery life, and reduce degradation costs. The effectiveness of the proposed scheduling strategy was verified through detailed simulation analysis, demonstrating improved wind power consumption capacity, slowed degradation of batteries and electrolyzers, and ultimately enhanced economic benefits for the system.