To develop a U-net deep learning method for breast tissue segmentation on fat-sat T1-weighted (T1W) MRI using transfer learning (TL) from a model developed for non-fat-sat images. The training dataset (N = 126) was imaged on a 1.5 T MR scanner, and the independent testing dataset (N = 40) was imaged on a 3 T scanner, both using fat-sat T1W pulse sequence. Pre-contrast images acquired in the dynamic-contrast-enhanced (DCE) MRI sequence were used for analysis. All patients had unilateral cancer, and the segmentation was performed using the contralateral normal breast. The ground truth of breast and fibroglandular tissue (FGT) segmentation was generated using a template-based segmentation method with a clustering algorithm. The deep learning segmentation was performed using U-net models trained with and without TL, by using initial values of trainable parameters taken from the previous model for non-fat-sat images. The ground truth of each case was used to evaluate the segmentation performance of the U-net models by calculating the dice similarity coefficient (DSC) and the overall accuracy based on all pixels. Pearson's correlation was used to evaluate the correlation of breast volume and FGT volume between the U-net prediction output and the ground truth. In the training dataset, the evaluation was performed using tenfold cross-validation, and the mean DSC with and without TL was 0.97 vs. 0.95 for breast and 0.86 vs. 0.80 for FGT. When the final model developed with and without TL from the training dataset was applied to the testing dataset, the mean DSC was 0.89 vs. 0.83 for breast and 0.81 vs. 0.81 for FGT, respectively. Application of TL not only improved the DSC, but also decreased the required training case number. Lastly, there was a high correlation (R > 0.90) for both the training and testing datasets between the U-net prediction output and ground truth for breast volume and FGT volume. U-net can be applied to perform breast tissue segmentation on fat-sat images, and TL is an efficient strategy to develop a specific model for each different dataset.