To solve the problem that the operation state of transformer is difficult to quantify, a method of quantitative evaluation and prediction of transformer operating state is proposed, which combines the information entropy of matter element and Support Vector Machine. In the evaluation, various hydrogen gases in the transformer operation are taken as the evaluation indexes and the three-dimensional cross compound element is constructed. The analytic hierarchy process (AHP) is used to determine the theoretical weight of the evaluation index, and the entropy method is used to determine the objective weight of the evaluation index, and the final weight is the joint weight of the theoretical weight and the objective weight. Transformer Health index is calculated by using complex element correlation entropy. In prediction, the grid search, genetic algorithm (GA) and particle swarm optimization (PSO) are used to optimize the parameters of Support Vector Machine. and the prediction model of Health index is established by SVM. Experiment results show that the Support Vector Machine based on Gauss kernel function and genetic algorithm has a prominent effect on the prediction of health index.