Aiming at the problem of material distribution delay caused by uncertainty of emergency degree in disaster relief work, an emergency logistics planning model with uncertainty of emergency degree was established. In the model, the Beta distribution was used to simulate the change of emergency degree in disaster area, and the total delay time and transportation time were taken as optimization objectives. A hybrid genetic algorithm based on emergency degree is designed for the problem, and a task redistribution algorithm based on emergency degree is used in the local search phase of genetic algorithm. According to the different characteristics of emergency degree of material demand points, the distribution route with delay is optimized. The experimental results show that the proposed model and algorithm have effect in tackling the objectives. Especially, the improvement in delay time obtained by the proposed algorithm is obvious compared with some classical algorithms. The performance of the model and algorithm is stable in a number of examples and quite robust.