One of the problems faced in implementing cellular manufacturing systems is machine-part group formation. This paper proposes machine-part grouping algorithms based on Self-Organizing Map(SOM) neural networks and K-Means algorithm in cellular manufacturing systems. Although the SOM spreads out input vectors to output vectors in the order of similarity, it does not always find the optimal solution. We rearrange the input vectors using SOM and determine the number of groups. In order to find the number of groups and grouping efficacy, we iterate K-Means algorithm changing k until we cannot obtain better solution. The results of using the proposed approach are compared to the best solutions reported in literature. The computational results show that the proposed approach provides a powerful means of solving the machine-part grouping problem. The proposed algorithm Is applied by simple calculation, so it can be for designer to change production constraints.