Three-ratio of the IEC is a convenient and effective approach for transformer fault diagnosis in the dissolved gas analysis (DGA). Fuzzy theory is used to preprocess the three-ratio for its boundary that is too absolute. As the same time, an improved quantum genetic algorithm IQGA (QGASAC) is used to optimize the weight and threshold of the back propagation (BP). The local and global searching ability of the QGASAC approach is utilized to find the BP optimization solution. It can overcome the slower convergence velocity and hardly getting the optimization of the BP neural network. So, aiming at the shortcoming of BP neural network and three-ratio, blurring the boundary of the gas ratio and the QGASAC algorithm is introduced to optimize the BP network. Then the QGASAC-IECBP method is proposed in this paper. Experimental results indicate that the proposed algorithm in this paper that both convergence velocity and veracity are all improved to some extent. And in this paper, the proposed algorithm is robust and practical.