The risk management for agricultural products supply chain is more complex than that for typical manufacturing supply chain. Agricultural production is vulnerable to severe weather such as heavy rain, cyclones, and cold wave, which challenges the matching of random output with random demand for agricultural products supply chains. The goal of this paper is to design an effective risk transfer mechanism for managing severe weather risks so as to ensure the stable operation of the agricultural products supply chain. We study the coordination of two-level agricultural products supply chain with a single company and a single farmer under the influence of severe weather. Taking rainstorm weather as an example, this paper designs a risk transfer mechanism based on weather index (rainfall) insurance: "rainfall index insurance + revenue sharing + risk transfer fee." It is found that this risk transfer mechanism can overcome distortion of the farmer's agricultural investment level under the influence of severe weather. When the contract parameters meet certain conditions, using the risk transfer mechanism can achieve the supply chain coordination and a win-win situation. More importantly, weather change does not affect the Pareto improvement of the company and the farmer under the risk transfer mechanism. In addition, we also find that the company can incentivize the farmer to purchase weather index insurance and use the insurance market to shift the severe weather risk encountered during the agricultural production to protect the company's and farmer's income and the stable operation of the supply chain.