This article presents an intelligent diagnosis and classification method for power transformer fault classification based on dissolved gas analysis: the support vector machine. It is a powerful algorithm for classification of faults that needs a limited set of small sampling data, a case of applications with non-linear behavior, and a high number of parameters; however, appropriate model parameters must be determined carefully. The selection of parameters has a direct effect on the machine's classification accuracy. In this study, a multi-layer support vector machine classifier is optimized by a grid search method and three heuristic approaches: (1) genetic, (2) differential evolution, and (3) particle swarm optimization algorithms. The performance analysis of the support vector machine hybridized with these optimization methods is demonstrated using the same classification set. The employed structure has five support vector machine layers, each of which uses a Gaussian kernel function due to its advantages of needing one parameter for optimization and providing excellent classification ability for non-linear data. The proposed approach gives highly accurate performance for diagnosis of power transformers. The support vector machine optimized with the particle swarm optimization algorithm has the best accuracy and requires less computational time compared to the other methods.