The outbreak of the COVID-19 (Corona Virus Disease 2019) has been becoming the most serious public health event in the world, threatening the health of hundreds of millions of people. The anti-pandemic policies mostly aim to prevent the spread at domestic and the import from abroad. In this paper, we discuss the issue of individual protection measures and customs quarantine strategy based on game theory. First, we develop a 2*2 Bayesian model and show that individual protection decisions depend on the size of excess payoff of taking protective measures (EPP). EPP is affected by the protection cost, the protective efficiency, the risk exposure and the information disclosure in this model. Then, we describe a repeated game between customs and airlines, and discuss the ideal strategy for customs to prevent the virus input. It comes out that a punishment mechanism for an airline is meaningful to prevent the import of the virus only if the discount rate of the airline is greater than the threshold. The threshold is positively correlated with the detection cost, and it is negatively correlated with the revenue of the airline and the testing reliability. We can also benefit from establishing a credit mechanism to give airlines that deviate from cooperation an opportunity to re-cooperate, especially for those in low risk areas. This study provides theoretical support for some government policies to prevent COVID-19, and underscores the significance of considering individual and organizational decision-making in health policy making.