Timely and effective distribution of relief materials is one of the most important aspects when fighting with a natural or a man-made disaster. Due to the sudden and urgent nature of most disasters, it is hard to make the exact prediction on the demand information. Meanwhile, timely delivery is also a problem. In this paper, taking the COVID-19 epidemic as an example, we propose an integrated method to fulfill both the demand estimation and the relief material distribution. We assume the relief supply is directed by government, so it is possible to arrange experts to evaluate the situation from aspects and coordinate supplies of different sources. The first part of the integrated method is a fuzzy decision-making process. The demand degrees on relief materials are estimated by extending COPRAS under interval 2-tuple linguistic environment. The second part includes the demand degrees as one of the inputs, conducts a hybrid distribution model to decide the allocation and routing. The key point of hybrid distribution is that each demand point could be visited by different vehicles and each vehicle could visit different demand points. Our method can also be extended to include both relief materials and medical staffs. A real-life case study of Wuhan, China is provided to illustrate the presented method.