Fibroglandular tissue (FGT) segmentation is a crucial step for quantitative analysis of background parenchymal enhancement (BPE) in magnetic resonance imaging (MRI), which is useful for breast cancer risk assessment. In this study, we develop an automated deep learning method based on a generative adversarial network (GAN) to identify the FGT region in MRI volumes and evaluate its impact on a specific clinical application. The GAN consists of an improved U-Net as a generator to generate FGT candidate areas and a patch deep convolutional neural network (DCNN) as a discriminator to evaluate the authenticity of the synthetic FGT region. The proposed method has two improvements compared to the classical U-Net: (1) the improved U-Net is designed to extract more features of the FGT region for a more accurate description of the FGT region; (2) a patch DCNN is designed for discriminating the authenticity of the FGT region generated by the improved U-Net, which makes the segmentation result more stable and accurate. A dataset of 100 three-dimensional (3D) bilateral breast MRI scans from 100 patients (aged 22-78 years) was used in this study with Institutional Review Board (IRB) approval. 3D hand-segmented FGT areas for all breasts were provided as a reference standard. Five-fold cross-validation was used in training and testing of the models. The Dice similarity coefficient (DSC) and Jaccard index (JI) values were evaluated to measure the segmentation accuracy. The previous method using classical U-Net was used as a baseline in this study. In the five partitions of the cross-validation set, the GAN achieved DSC and JI values of 87.0 ± 7.0% and 77.6 ± 10.1%, respectively, while the corresponding values obtained through by the baseline method were 81.1 ± 8.7% and 69.0 ± 11.3%, respectively. The proposed method is significantly superior to the previous method using U-Net. The FGT segmentation impacted the BPE quantification application in the following manner: the correlation coefficients between the quantified BPE value and BI-RADS BPE categories provided by the radiologist were 0.46 ± 0.15 (best: 0.63) based on GAN segmented FGT areas, while the corresponding correlation coefficients were 0.41 ± 0.16 (best: 0.60) based on baseline U-Net segmented FGT areas. BPE can be quantified better using the FGT areas segmented by the proposed GAN model than using the FGT areas segmented by the baseline U-Net.