This paper studies effective traceable feature representation learning in the view of distribution transformation, termed FeatsFlow, by proposing a distribution-aware learning framework combining the discriminating model with a normalizing flow-based model. The process can be regarded as a series of feature distribution transformations, from the input images to the expected results. Focusing on the learned representation of the target model, we take full advantage of the invertible nature of normalizing flows and learn the practical and traceable feature representation for target goals. Considering that it is difficult to model the traceable process for feature extraction, we propose an effective model by combining a general discriminating model with normalizing flows for traceable feature extraction. The normalizing flows module is added to the original model in a plug-in mode, which is convenient to make it available for effective and traceable feature learning. Thus we can obtain an effective and traceable representation distribution. Extensive experiments are conducted on our proposed representation learning model for the image classification task, and the experimental results illustrate that our proposed model is adequate for traceable representation learning. The most important is that we present a distribution-aware representation learning approach, which makes it possible to conduct and understand feature representation learning at the feature level.