Automated segmentation of liver tumors in contrast-enhanced abdominal computed tomography (CT) scans is essential in assisting medical professionals to evaluate tumor development and make fast therapeutic schedule. Although deep convolutional neural networks (DCNNs) have contributed many breakthroughs in image segmentation, this task remains challenging, since 2D DCNNs are incapable of exploring the inter-slice information and 3D DCNNs are too complex to be trained with the available small dataset. In this paper, we propose the light-weight hybrid convolutional network (LW-HCN) to segment the liver and its tumors in CT volumes. Instead of combining a 2D and a 3D networks for coarse-to-fine segmentation, LW-HCN has a encoder-decoder structure, in which 2D convolutions used at the bottom of the encoder decreases the complexity and 3D convolutions used in other layers explore both spatial and temporal information. To further reduce the complexity, we design the depthwise and spatiotemporal separate (DSTS) factorization for 3D convolutions, which not only reduces parameters dramatically but also improves the performance. We evaluated the proposed LW-HCN model against several recent methods on the LiTS and 3D-IRCADb datasets and achieved, respectively, the Dice per case of 73.0% and 94.1% for tumor segmentation, setting a new state of the art.