The U-Net deep learning is a feasible method for segmentation of breast and fibroglandular tissue on non-fat-suppressed (non-fat-sat) T1-weighted images. Whether it can work on fat-sat images, which are more commonly used for diagnosis, is studied. Three datasets were used: 126 Training, 62 Testing Set-A, and 41 Testing Set-B. The model was developed without and with transfer learning based on parameters in the previous model developed for non-fat-sat images. The results show that U-Net can also achieve a high segmentation accuracy for fat-sat images, and when training case number is small, transfer learning can help to improve accuracy.