It is difficult to extract effective features and select model parameters when using a support vector machine (SVM) for transformer fault diagnosis. A transformer fault diagnosis method based on feature extraction and an improved northern goshawk optimization (INGO) algorithm optimized SVM is proposed. First, kernel principal component analysis (KPCA) is used to conduct feature fusion and low dimensional sensitive feature extraction for the 21 dimensional candidate feature. Secondly, strategies such as good point set, random opposition-based learning, and dimensional cross learning are used to improve the northern goshawk optimization (NGO) algorithm. The performance of the INGO algorithm is tested using two typical test functions, verifying its superiority. Then, based on the low dimensional sensitive feature extracted by KPCA, INGO is used to optimize the parameters of the SVM, and a transformer fault diagnosis model is established based on KPCA feature extraction and INGO-SVM. Finally, simulation and comparative experiments are conducted on different transformer fault diagnosis models. The results show that the proposed method has high accuracy and good stability in fault diagnosis, and is more suitable for transformer fault diagnosis.