Artificial intelligence is the general trend in the field of power equipment fault diagnosis. However, limited by operation characteristics and data defects, the application of the intelligent diagnosis method in power transformers is still in the initial stage. To fill this research gap, in this article, a novel double-stacked autoencoder (DSAE) is proposed for a fast and accurate judgment of power transformer health conditions with an imbalanced data structure. Three problems affecting the diagnosis effectiveness are overcome by a DSAE framework, an aging-tolerance criterion, and an advanced sparse deep clustering network. The proposed DSAE method is validated by two case studies based on an actual power transformer dataset. The results indicate that the proposed DSAE method can achieve a fairly reliable diagnosis with a higher accuracy and less time than the other methods, which demonstrates the superiority and effectiveness of the proposed approach.