In the face of today's frequent natural disasters, it is important to study how to balance the fairness and efficiency of post-disaster emergency supplies distribution from a system-wide perspective for the efficient implementation of post-disaster relief. The hierarchical analysis method was used to assign weights to the measurement indicators for demand urgency. A joint truck-drone distribution path optimization model for emergency supplies was conducted considering the degree of demand urgency, with the objective of maximizing the ranking index of demand urgency at the disaster-stricken points and minimizing the total cost of distribution with delay penalties, and an improved nondominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) algorithm was developed to solve the model. The results show that the model is able to meet the distribution demands of emergency supplies at the disaster site under different degrees of urgency, and the improved NSGA-Ⅱ algorithm has a better effect on the optimization of the objective function, which can provide a scientific reference for decision makers to formulate a reasonable distribution plan for emergency supplies.