As the COVID-19 pandemic evolves, the public has gradually established the habit of buying medical supplies through the Internet. It is urgent to develop an efficient and green medicine distribution mode. A location-routing two-stage mathematical programming model considering dynamic demand is established to solve the problem of location planning and distribution route designing of pharmaceutical pre-warehouse. The NSGA-III algorithm is used to solve the initial optimization stage and dynamic optimization stage respectively. The optimal scheme is selected using the fuzzy clustering method as the initial state of the dynamic optimization stage. Comparing with the NSGA-II algorithm for time, Spacing, HRS and PR, the NSGA-III runs faster, and gets more uniform solution set distribution and better convergence effect. Finally, the influence of the total budget change of fixed cost on the three objective functions of cost, time and carbon emission are calculated to test the sensitivity of the model and algorithm. It indicates that the third-party drug delivery enterprises are more suitable to use small or medium-sized vehicles to complete the delivery task and set relatively abundant location budget.