Single-frame infrared small target detection (IRSTD) aims to extract targets from background clutter and distinguish them from noise. In recent years, semantic segmentation deep learning methods such as CNNs have made many breakthroughs in the field of IRSTD. However, there are limitations to this method; for example, the targets tend to be too dim, and heavy background clutter exists. To further improve the accuracy of IRSTD, we propose a novel curvature half-level fusion network (CHFNet) for IRSTD. First, we developed a half-level fusion (HLF) block as a new cross-layer feature fusion module. With the HLF block, the network excavates the half-level features between two levels of features, thus ensuring that each feature of the levels has minimal distortion. Given that even dim targets have certain curvature features, we calculated the weighted mean curvature of the image to obtain the attention of the boundary, then fused it with the features of each level to detect the edges of targets. In comparison, the prediction results of the proposed CHFNet on the NUAA-SIRST dataset were more complete and better preserved edge targets.