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Climate change leads to the frequent occurrence of natural disasters. It has had a severe impact on agricultural economic growth in China. Based on data in China from 2004 to 2020, this paper uses a fixed-effect model to discuss the effects of natural disasters on agricultural economic growth. The empirical results are as follows. (1) Natural disasters negatively affect agricultural economic growth. The regression coefficient of natural disasters on agricultural economic growth is −0.1183. (2) The inhibition of agricultural economic growth by natural disasters is more prominent in areas with low government attention and average agricultural production conditions. (3) The mechanism analysis shows that natural disasters inhibit agricultural economic growth through channels that cause the spread of diseases and pests. (4) Expanding the scale of agricultural insurance can prevent the impact of natural disasters on agricultural economic growth. This research provides policy recommendations for preventing the negative impacts of natural disasters. Agricultural producers should raise awareness of disaster management and improve the accuracy of disaster warning mechanisms. • This paper measures the level of natural disasters in China. • This paper expands the application field of functional data analysis methods. • This paper examines the mechanism of natural disasters affecting agricultural economic growth. • This paper provides policy suggestions for ensuring agricultural economic growth. [ABSTRACT FROM AUTHOR]