The development of green hydrogen energy technology is one of the promising pathways towards achieving the carbon peaking and carbon neutrality goals. Green ammonia production has emerged as the primary method of implementing green hydrogen energy, due to its advancement in storage and transportation capabilities. Particularly, there is a considerable focus on green ammonia production from renewable sources, such as wind or solar. In this paper, a method for optimizing the system-level green ammonia production system based on largescale wind power generation is proposed. The processes of power generation, hydrogen generation and green ammonia production, as well as the safety conditions for their operation are all taken into account. With the goal of maximizing the total economic benefit, a mixed-integer programming model is developed. The proposed model is implemented in a case study from our project. Using the real-world data from the “Three North” region in China, the optimal sizing of hydrogen production electrolyzer, energy storage battery, hydrogen storage and green ammonia production capacity are obtained. The results demonstrate that the proposed method can globally optimize the system while ensuring the safety constraints, thus effectively improving the economy of the green ammonia production system.