Abstract: A new multi level hierarchical interconnection network with constant degree is proposed for massively parallel processing systems. The proposed interconnection network is named fully connected cubic network （FCCN）. FCCN has a number of excellent properties, such as high scalability and modularity. An m level FCCN is constructed by “fully connecting” 8 （ m-1） FCCNs . Both the diameter and the average hop distance are in the order of the cubic root of the number of nodes. Owing to the highly scalable structure, the routing algorithm proposed is very simple to implement. The calculating results of a practical parallel processing system connected by FCCN show that FCCN is a high efficient interconnection network.