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An unsupervised competitive learning algorithm based on the classical k-means clustering algorithm is proposed. The proposed learning algorithm called the centroid neural network (CNN) estimates centroids of the related cluster groups in training date. This paper also explains algorithmic relationships among the CNN and some of the conventional unsupervised competitive learning algorithms including Kohonen's self-organizing map and Kosko's differential competitive learning algorithm. The CNN algorithm requires neither a predetermined schedule for learning coefficient nor a total number of iterations for clustering. The simulation results on clustering problems and image compression problems show that CNN converges much faster than conventional algorithms with compatible clustering quality while other algorithms may give unstable results depending on the initial values of the learning coefficient and the total number of iterations