Aiming at the difficulty in selecting transformer fault features and the low accuracy of diagnosis model, a hybrid fault feature selection method is proposed, and the deep hybrid kernel limit learning machine （DHKELM） is optimized by the improved northern Goshawk optimization algorithm （INGO） to realize transformer fault diagnosis. Firstly, a 24-dimensional transformer fault feature set is constructed based on correlation ratio method. From the perspective of linear correlation and nonlinear correlation, Pearson correlation coefficient and mutual information method are used to filter out the features with low correlation. Secondly, Logistic chaotic mapping, stochastic reverse learning and adaptive t-distribution mutation are introduced to improve NGO algorithm, so as to improve its optimization performance. Then, INGO algorithm is used to filter the retained features for the second time to obtain the optimal input features. Finally, the automatic encoder of the extreme learning machine is introduced into the hybrid core extreme learning machine, and the DHKELM diagnosis model is established. The initial parameters of the DHKELM model are optimized by INGO, and the INGO-DHKELM transformer fault diagnosis model is completed. Experiments show that compared with the conventional feature selection method, the input features selected by the hybrid fault feature selection method can effectively improve the diagnosis accuracy. Compared with other optimized diagnosis models, INGO-DHKELM has higher accuracy and better stability.