Abstract: The graph embedding is an important technique to study the capability of multiprocessor interconnection networks simulating other networks. The property of cycle embedding of a kind of interconnection networks recently introduced——the Mbius cubes is discussed. They are hypercube variants which give better properties than hypercubes. For example, the diameter of the n dimensional Mbius cube M n is about one half that of the n dimensional hypercube, the expected distance of M n is about two thirds that of the n dimensional hypercube, etc..It is proved that the Mbius cubes have another better property than hypercubes, i.e., any cycle of length l（4≤l≤2 n） can be embedded into the n dimensional MAKo¨D4bius M n（n≥2） and gives a constructing procedure, and also proves that the capability of M n’ s simulating ring networks is higher than that of the n dimensional hypercube （hypercubes do not contain odd cycles）.