Accurate liver tumor segmentation from multiphase CT images is a prerequisite for data-driven tumor analysis. This study presents a domain-adaptive transformer (DA-Tran) network to segment liver tumors from each CT phase. First, a DA module is designed to produce domain-adapted feature maps from noncontrast-enhanced (NC)-phase, arterial (ART)-phase, portal venous (PV)-phase, and delay-phase (DP) images. Then, these domain-adapted feature maps are integrated using 3D transformer blocks to catch patch-structured similarity information and global context attention. Finally, the attention fusion decoder (AFD) integrates features from different branches to generate a more refined prediction. Extensive experimental results demonstrate that DA-Tran achieves state-of-the-art tumor segmentation results, i.e., a Dice similarity coefficient (DSC) of 87.00% and a 95% Hausdorff distance (HD95) of 5.10 mm on a clinical dataset (DB1). Additionally, DA-Tran consistently outperforms other cutting-edge methods on another multiphase liver tumor dataset (DB2). The DA module and transformer blocks can boost the co-segmentation performance and make DA-Tran an ideal solution for multiphase liver tumor segmentation.