Since 2019, the global COVID-19 outbreak has emerged as a crucial focus in healthcare research. Although RT-PCR stands as the primary method for COVID-19 detection, its extended detection time poses a significant challenge. Consequently, supplementing RT-PCR with the pathological study of COVID-19 through CT imaging has become imperative. The current segmentation approach based on TVLoss enhances the connectivity of afflicted areas. Nevertheless, it tends to misclassify normal pixels between certain adjacent diseased regions as diseased pixels. The typical Binary cross entropy(BCE) based U-shaped network only concentrates on the entire CT images without emphasizing on the affected regions, which results in hazy borders and low contrast in the projected output. In addition, the fraction of infected pixels in CT images is much less, which makes it a challenge for segmentation models to make accurate predictions. In this paper, we propose COVID-CT-H-UNet, a COVID-19 CT segmentation network to solve these problems. To recognize the unaffected pixels between neighbouring diseased regions, extra visual layer information is captured by combining the attention module on the skip connections with the proposed composite function Bi-category Hybrid Loss. The issue of hazy boundaries and poor contrast brought on by the BCE Loss in conventional techniques is resolved by utilizing the composite function Bi-category Hybrid Loss that concentrates on the pixels in the diseased area. The experiment shows when compared to the previous COVID-19 segmentation networks, the proposed COVID-CT-H-UNet's segmentation impact has greatly improved, and it may be used to identify and study clinical COVID-19.