Abstract: The Mbius cube is a hypercube variant. It has some superior properties to the hypercube. However, like the hypercube, it is also an n regular graph with 2 n nodes. So, it is necessary to double the number of nodes to upgrade the Mbius cube. In order to solve this problem, the topological structure of the Mbius cube with 2 n nodes is modified and the interconnection network the super Mbius cube is obtained, which contains arbitrary number of nodes. It is proved that the super Mbius cube preserves such fine properties as high connectivity, logarithm diameter,and node degree,and that when its number of nodes N is equal to 2 n +2 n-1 , the 0 type super Mbius cube is an （ n +1） regular graph; further more, because the super Mbius cube has arbitrary number of nodes, it needs only to add arbitrary number of nodes to upgrade itself, thus overcoming the shortcoming of the Mbius cube that it is necessary to double the number of nodes to upgrade it.