For warehouses storing fixed types of goods, the work aims to design a series of cargo packaging container dimensions so that each type of cargo can be contained in the most suitable container of the designed dimensions to improve the transportation and storage efficiency of warehouses. According to the problem description, with the isomorphic packing of single container as the basis and the average value of the best space utilization rate of all cargoes in the containers of different dimensions as the objective function, the genetic container packing algorithm was employed to solve the objective function, and the grey wolf optimization algorithm (GA-GWO) was used to optimize the design of the container dimensions. Based on this, the greedy container packing algorithm was introduced to improve the original algorithm (GR-GA-GWO). To verify the practicality of the algorithm, 15 types of cargoes from Company A's warehouse were taken as samples, and four container dimension optimization design problems were designed. The results solved by GA-GWO could complete the cargo packaging container dimension design, but the calculation time was relatively long. The solution results of GR-GA-GWO reduced the objective function by 2.85%-5.34% compared to GA-GWO, but saved 40.98%-60.49% of the time, which was an effective algorithm improvement. The proposed method for optimizing the design of cargo packaging container dimensions based on the grey wolf optimization algorithm can provide a reference for the cargo packaging container dimension design of various types of warehouses.