In medical imaging, MR T1 in-phase and out-phase images, when combined, produce a clear representation of pure water, aiding in tissue analysis and diagnosing conditions like fatty liver. However, accurately segmenting the liver from these complex images poses challenges due to fuzzy boundaries and variable appearances. To address this, deep learning techniques, particularly the U-Net architecture, have shown promise. Different variants of U-Net, such as Residual U-Net, Attention U-Net, and RA-UNet, have been developed to improve liver segmentation accuracy. In our study, we applied these U-Net variants to segment the liver from MR T1 fused images. Among them, the Attention U-Net model demonstrated superior performance, achieving a Mean Intersection over Union (IoU) value of 0.9513. This indicates its effectiveness in accurately delineating liver boundaries and its potential for enhancing clinical tasks like surgical planning and postoperative evaluation.