Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-ANMI, a new efficient algorithm for clustering categorical data. The k-ANMI algorithm works in a way that is similar to the popular k-means algorithm, and the goodness of clustering in each step is evaluated using a mutual information based criterion (namely, Average Normalized Mutual Information-ANMI) borrowed from cluster ensemble. Experimental results on real datasets show that k-ANMI algorithm is competitive with those state-of-art categorical data clustering algorithms with respect to clustering accuracy.