In this work, a generalized topology of block shift networks (BSNs), named generalized block shift network (GBSN), is propose or interconnection networks in clusters. The BSNs possess many desirable topological features, such as flexibility in node degree, small diameter and average distance, and easy VLSI implementation. However, the regular structure of each block in the BSN is not suitable for the networks in clusters that usually have arbitrary number of nodes. The proposed GBSN offers a balance between regularity and irregularity of the interconnection networks for clusters. We also analyze the embedding of the BSN into the GBSN, and discuss the versatility of the GBSN in terms of slowdown factors compared to the BSN.