Power transformers are the vital and expensive components of the power system. Timely identifying and diagnosing the transformer faults is critical to maintaining the stability of the power grid. As a sensitive and economical tool, the frequency response analysis (FRA) method has been widely employed to detect winding faults. However, it is still a challenge to accurately identify the fault types and degrees only by the FRA method. In this article, a new diagnosis method that combines the FRA method with a kernelbased extreme learning machine (KELM) optimized by a seagull optimization algorithm (SOA), is proposed to diagnose the fault types and degrees of the winding. First, a series of FRA tests are performed on a laboratory winding model under three different faults to obtain the FRA dataset. Furthermore, various numerical indices are applied to extract the characteristics of FRA signatures to train the SOA-KELM model. Then, the trained SOA-KELM model is utilized to classify fault types and degrees of the winding. Finally, the feasibility and superiority of SOA-KELM are verified by comparing with SOA optimized support vector machine (SOA-SVM) and random forest (SOA-RF), particle swarm optimization (PSO) algorithm optimized KELM (PSO-KELM), PSO-SVM, PSO-RF, SVM, RF, and KELM from the aspects of diagnosis accuracy and running time. The comprehensive comparison results show that SOA-KELM has the best diagnosis performance.