Diagnosis techniques based on the dissolved gas analysis(DGA) have been developed to detect incipient faults in power transformers. Various methods exist based on DGA such as IEC, Roger, Dornenburg, and etc. However, these methods have been applied to different problems with different standards. Furthermore, it is difficult to achieve an accurate diagnosis by DGA without experienced experts. In order to resolve these drawbacks, this paper proposes a novel diagnosis method using fuzzy clustering and a radial basis neural network(RBFNN). In the neural network, fuzzy clustering is effective for selecting the efficient training data and reducing learning process time. After fuzzy clustering, the RBF neural network is developed to analyze and diagnose the state of the transformer. The proposed method measures the possibility and degree of aging as well as the faults occurred in the transformer. To demonstrate the validity of the proposed method, various experiments are performed and their results are presented.