We present an efficient dynamic algorithm for clustering undirected graphs, whose edge property is changing continuously. The algorithm maintains clusters of high quality in presence of insertion and deletion (update) of edges. The algorithm is motivated by the minimum-cut tree based partitioning algorithm of [3] and [4]. It takes O(k3 ) time for each update processing, where k is the maximum size of any cluster. This is the worst case time complexity, and in general update time taken is much less. The clusters satisfy the bicriteria for quality guarantee proposed in [3].