Liver cancer is a kind of malignant tumor, early screening and accurate detection is the key to improve the treatment effect and prolong the survival of patients. In view of the difficulty of accurately detecting complex and variable liver cancer using single-phase computed tomography (CT) images, in this paper, a dual-phase CT method for liver cancer detection based on fully convolutional one-stage object detection (FCOS) is proposed. Firstly, the dual-phase liver CT quadtuple network is constructed and used to match the dual-phase liver CT slices to ensure the consistency of liver position between different phases and lay a foundation for the subsequent detection of liver cancer. Secondly, FCOS network is improved to receive input of dual-phase CT images, attention-based feature fusion (AFF) module is designed and inserted, and feature fusion with mixed attention is performed at the same time to improve the accuracy of liver cancer detection. The experimental results show that the average precision (AP) of the improved algorithm on the data set in this paper reaches 78.56%, which is 4.9% higher than that of the single-phase FCOS network, showing better performance.