In recent years, the frequent occurrence of public health emergencies has had a significant impact on people’s life. The study of emergency logistics has also attracted scholars’ attention. Therefore, matching emergency materials’ supply and demand quickly, which meets urgency and satisfaction, is the purpose of this paper. This paper used the Metabolism Grey Model (1,1) (GM (1,1)) and the material demand prediction model to predict the number of infections and material demand. Besides, we established a bi-objective optimization model by constructing a profit and loss matrix and a comprehensive utility perception matrix. The results show that the method is helpful in matching the optimal supply and demand decision quickly on the basis of meeting urgency and satisfaction. The method is helpful in improving the fairness of emergency material distribution, which could better protect people’s livelihoods.