Frequency response analysis (FRA) demonstrates significant advantages in the diagnosis of transformer winding faults. The instrument market desires intelligent diagnostic functions to ensure that the FRA technique is more practically useful. In this paper, a hierarchical dimension reduction (HDR) classifier is proposed to identify types of typical incipient winding faults. The classifier procedure is hierarchical. First, measured frequency response (FR) curves are preprocessed using binarization and binary erosion to normalize FR data. Second, the pre-processed data are divided into groups according to the definition of dynamic frequency sub-bands. Then, hybrid algorithms comprised of two conventional and two novel quantitative indices are used to reduce the dimension of the FR data and extract the features for identifying typical types of transformer winding faults. The classifier provides an integration of a priori expertise and quantitative analysis in the furtherance of the automatic identification of FR data. Twenty-six sets of FR data from different types of power transformers with multiple types of winding faults were collected from an experimental simulation, literature, and real tests performed by a grid company. Finally, real case studies were conducted to verify the performance of the HDR classifier in the automatic identification of transformer winding faults.