The group formation problem of the machine and part is a very important issue in the planning stage of cellular manufacturing systems. This paper investigates Self-Organizing Map(SOM) neural networks approach to machine-part grouping problem. We present a two-phase algorithm based on SOM for grouping parts and machines. SOM can learn from complex, multi-dimensional data and transform them into visually decipherable clusters. Output layer in SOM network is one-dimensional structure and the number of output node has been increased sufficiently to spread out the input vectors in the order of similarity. The proposed algorithm performs remarkably well in comparison with many other algorithms for the well-known problems shown in previous papers.