Substation facilities have become extremely large and complex parts of electric power systems. The development of condition monitoring and diagnosis techniques has been a very significant factor in the improvement of substation transformer security. This paper presents a method to analyze the cause, the degree, and the aging process power transformers by the Self Organizing Map (SOM) method. Dissolved gas data were non-linearly transformed by the sigmoid function in SOM that works much the same way as the human decision making process. The potential for failure and the degree of aging of normal transformers are identified by using the proposed quantitative criterion. Furthermore, transformer aging is monitored by the proposed criterion for a set of transformers. To demonstrate the validity of the proposed method, a case study is performed and its results are presented.