Abstract: With the development of biological sciences and communication engineering, a lot of phenomena about cluster synchronization arediscovered and investigated. However, because of the complexity of network, the theoreticalresults about cluster synchronization are very limited. In this paper,for the case that the number of every cluster is equal to m, a coupled weightnetwork is constructed, and a sufficient condition about thesynchronization with n clusters is obtained. The effectiveness of the methods is illustrated by an example.