When huge disasters strike, the afflicted areas need help from all sides. However, it is difficult for relevant departments to quickly obtain relief needs of disaster areas and accurately distribute relief materials on demand. To solve this problem, this paper proposes a relief demands urgency evaluation approach which integrates Natural Language Processing (NLP), Analytic Hierarchy Process (AHP), EWM (the entropy weight method), and the Grey Relational Technique for Order Preference by Similarity to Ideal Solution (Grey TOPSIS). First, the evaluation index system of disaster relief demand is constructed from four aspects, emergency support demands, emergency rescue demands, basic life support demands, and public infrastructure support demands. Then, the indices are assigned based on social media data and real-time reports, and the weight is assigned based on AHP and EWM. At last, the Grey TOPSIS is used to evaluate the relief demand urgency of different disaster areas. Due to the high timeliness of social media data, our approach is efficient. Taking Typhoon Lekima as an example, we evaluate the disaster relief needs of cities in Zhejiang Province, Jiangsu Province, and Shandong Province and compare the evaluation values with official post disaster statistics. Results show that the urgency of disaster relief needs calculated by our proposed method is significantly correlated with actual economic losses. Moreover, the method can identify specific disaster relief needs, so as to improve the timeliness and accuracy of emergency rescue.