In this paper, a new multi-cell lattice honeycomb paperboard was designed based on the expansion manufacturing process, aiming to improve the load-bearing capacity and energy absorption of the honeycomb paperboard. Quasi-static axial crush experiments were conducted on multi-cell lattice honeycomb paperboard (MHC) and standard honeycomb paperboard (HC), and the out-of-plane crushing response and energy absorption of MHC and HC are compared. The deformation mode of MHC is discussed in detail. A typical folding element is selected, and a theoretical model is developed to predict the plateau stress of the MHC. The results show that under the same structural and cell length dimensions, the peak stress of MHC is 3.3 times higher than that of HC, the plateau stress and energy absorption are 3.9 times higher than that of HC. Under the same relative density conditions, the peak stress of MHC is enhanced by 10% over HC, and the plateau stress and energy absorption are enhanced by 30% and 29%, respectively. The predicted plateau stress from the theoretical model compares well with the experimental values. The great potential for industrial applications of multi-cell lattice honeycomb paperboard based on an expansion manufacturing process is demonstrated, with minimal modifications to the manufacturing process but with a significant increase in load-bearing capacity and energy absorption. These results could be used as a reference for the design and improvement of honeycomb structures and other similar structures.