Clustering is an useful method to classify objects into subsets that have some meaning in the context of a particular problem and has been applied in variety of fields, customer relationship management, data mining, pattern recognition, and biotechnology etc. This paper addresses the unknown K clustering problems and presents a new approach based on a coevolutionary algorithm to solve it. Coevolutionary algorithms are known as very efficient tools to solve the integrated optimization problems with high degree of complexity compared to classical ones. The problem considered in this paper can be divided into two sub-problems; finding the number of clusters and classifying the data into these clusters. To apply to coevolutionary algorithm, the framework of algorithm and genetic elements suitable for the sub-problems are proposed. Also, a neighborhood-based evolutionary strategy is employed to maintain the population diversity. To analyze the proposed algorithm, the experiments are performed with various test-bed problems which are grouped into several classes. The experimental results confirm the effectiveness of the proposed algorithm.