Precision therapy for liver cancer necessitates accurately delineating liver sub-regions to protect healthy tissue while targeting tumors, which is essential for reducing recurrence and improving survival rates. However, the segmentation of hepatic segments, known as Couinaud segmentation, is challenging due to indistinct sub-region boundaries and the need for extensive annotated datasets. This study introduces LiverFormer, a novel Couinaud segmentation model that effectively integrates global context with low-level local features based on a 3D hybrid CNN-Transformer architecture. Additionally, a registration-based data augmentation strategy is equipped to enhance the segmentation performance with limited labeled data. Evaluated on CT images from 123 patients, LiverFormer demonstrated high accuracy and strong concordance with expert annotations across various metrics, allowing for enhanced treatment planning for surgery and radiation therapy. It has great potential to reduces complications and minimizes potential damages to surrounding tissue, leading to improved outcomes for patients undergoing complex liver cancer treatments.