This paper discussed the issue of three-dimensional packing of single-sized cuboid items, namely, arrangement of single-sized cuboid items in a given box as much as possible. Using the hierarchical loading scheme to simplify the loading operation, firstly the dynamic programming technique was used to determine the arrangement of cuboids in all layers, then the one-dimensional knapsack problem was solved to determine the optimal combination of the layers in the box, thus obtaining the optimal loading scheme. The algorithm in this paper was compared with other three-dimensional packing algorithms in literatures. The experimental results showed that the algorithm in this paper can work out a loading scheme which increased the utilization rate of box space from 98.10% to 99.14%. This algorithm can achieve a loading scheme with simple operation and high utilization rate of box space in reasonable time.