The method of Support Vector Machine (SVM) based on Dissolved Gas Analysis (DGA) has been studied in the field of power transformer fault diagnosis. However, there are still some shortcomings, such as the fuzzy boundaries of DGA data, and SVM parameters are difficult to determine. Therefore, this paper proposes a power transformer fault diagnosis method based on Kernel Principal Component Analysis (KPCA) and a hybrid improved Seagull Optimization Algorithm to optimize the SVM (TISOA-SVM). Firstly, KPCA is used to extract features from DGA feature quantities. In addition, TISOA is further proposed to optimize the SVM parameters to build the optimal diagnosis model based on SVM. For the SOA, three improvement methods are proposed. An improved tent map is used to replace the original population initialization to improve population diversity. In addition, the nonlinear inertia weight and random double helix formula are proposed to improve the optimization accuracy and efficiency of the SOA. Then, benchmarking functions are used to test the optimization performance of TISOA and six algorithms, and the results show that TISOA has the best optimization accuracy and convergence speed. Finally, the fault diagnosis method based on KPCA and TISOA-SVM is obtained, and it is noteworthy that three examples are tested to verify the diagnostic performance of the proposed method. These results show that the proposed method has higher diagnostic accuracy, shorter diagnosis time, stronger significance and validity than other methods. Therefore, a research idea is provided for solving practical engineering problems in the field of fault diagnosis.INDEX TERMS Power transformer, fault diagnosis, kernel principal component analysis, support vector machine, hybrid improved seagull optimization algorithm.