Abstract: Clustering is an important tool for data mining. Its aim is to assign the points into groups that are homogeneous within a group and heterogeneous between groups. Many works of clustering methods have been researched in diverse machine learning fields. An efficient algorithm of clustering is K-means algorithm. This is a partitioning method. Also K-means algorithm has offered good clustering results. As well other clustering methods, K-means algorithm has some problems. One of them is optimal selection of the number of clusters. In K-means algorithm, the number of cluster K is determined by the art of researchers. In this study, we propose a co-evolutionary K-means(CoE K-means) algorithm for overcoming the problem of K-means algorithm. Our CoE K-means algorithm combines co-evolutionary computing into K-means algorithm. In our experimental results, we verify improved performances of CoE K-means algorithm using simulation data.