When loaded parallel to the prismatic cells (out-of-plane), honeycombs and re-entrant honeycombs exhibit high initial stiffness and peak force, followed by a force reduction as progressive failure occurs. The high initial peak force and large post-peak force reduction are undesirable for energy absorption purposes. In this study a graded honeycomb structure based on origami is proposed in an effort to lower the peak force, increase the energy absorption capacity and tune the stiffness throughout the loading process. The grading is achieved through a developable origami crease pattern that utilises the typical honeycomb expansion manufacturing technique. The crease pattern has one degree of freedom and is constructed from a repetition of a modified Miura-ori unit. A kinematic study of the crease pattern is completed, highlighting the simple geometric parameters that can be altered to tune the structure. Quasi-static numerical simulations are then used to investigate the interaction between these simple geometric parameters, the energy absorption capacity and the stiffness throughout the loading process. Compared to honeycomb and re-entrant honeycomb tubes, it has been found that a reduction in the peak force, increase in energy absorption capacity and tunable stiffness can be achieved.