Due to the spread of COVID-19, the public health crisis is bound to have a huge impact on the world economy and international trade. How to study the import and export strategies under the coronavirus pandemic has become a major issue that many scholars need to solve urgently. Therefore, a two-stage game model is constructed, and the reverse solution method is used to obtain the optimal output of enterprises in importing countries and exporting countries before and after the outbreak of pandemic, as well as the optimal subsidies for enterprises from exporting countries and the optimal import quarantine rate for importing countries. Based on the game between the two countries without the pandemic outbreak, the impact of the pandemic on the output, profits, and social welfare of enterprises in the two countries was compared. Enterprises in exporting countries face double threats from the pandemic and import quarantine fees. The increase in import quarantine fees reduces the social welfare of exporting countries. In order to effectively control the spread of the pandemic, subsidies are an effective means to restore exports to normal. Reasonable collection of import quarantine fees by importing countries can promote bilateral trade, but an excessive collection will be counterproductive. The governments of exporting countries should establish emergency mechanisms and relevant subsidy policies, and enterprises should continuously improve their competitiveness. At the same time, countries should abandon the concept of trade protection and negotiate and cooperate to jointly deal with the pandemic.