With the increasing global concern regarding public health, accurate diagnosis and treatment of diseases have become critical. In the context of liver computed tomography (CT) image diagnosis, obtaining precise liver segmentation output samples can save consultation time and reduce the risk of misdiagnosis. We propose a full-scale connected attention-aware segmentation network, called Attention UNet3+. To fully leverage semantic information at different scales, we redesign the depth supervised decoder and adopt a full-scale skip connection, which can effectively extract features from different layers thus increasing accuracy. The proposed Attention UNet3+ model uses an attention gate connection instead of the skip connection, which effectively suppresses irrelevant regions and highlights salient features of specific local regions during feature extraction, therefore, improving the segmentation accuracy. Additionally, the classification-guided module enhances the liver boundary and reduces over-segmentation of non-liver regions, obtaining accurate segmentation results. Our experimental evaluation on the medical image computing and computer assisted intervention Liver Tumor Segmentation Challenge 2017 dataset shows that the proposed Attention UNet3+ outperforms other improved UNet algorithms for liver image segmentation by a minimum of 2.9% in intersection over union and a minimum of 1.1% in Dice.