In this paper, we presented an extended family of Miura-ori structures with programmable multi-step deformation via arraying and mirroring. We found that there is a competitive relationship between thickness gradient and structural gradient for these origami structures. Furthermore, we demonstrate that the multi-step deformation can be designed by altering the geometrical parametric and the order of these origami structures and the number of deformation stages will change with the change of the thickness gradient. Therefore, the current study can be used to construct novel origami metamaterials for engineering applications, such as energy absorbers for both light and heavy impacts.