It is important to minimize the number of disk accesses which is necessary to transfer data in disk into main memory when processing transactions in physical database design. A vertical file partitioning method is used to reduce the number of disk accesses by partitioning relations vertically and accessing only necessay fragments. In this paper, SOFM(Self-Organizing Feature Maps) network is used to solve vertical partitioning problems. This paper shows that SOFM network is efficient in solving vertical partitioning problem by comparing approximate solution of SOFM network with optimal solution of N-ary branch and bound method. And this paper presents a heuristic algorithm for allocating duplicate attributes to vertically partitioned fragments. As branch and bound method requires particularly much computing time to solve large-sized problems, it is shown that SOFM network is able to overcome this limitation of branch and bound method and solve large-sized problems efficiently in a short time.