Imaging blood vessel networks is useful in many biomedical applications, such as injection-assist, cancer detection, various surgery, and vein identification. In NIR (near-infrared) transillumination imaging, we can visualize the subcutaneous blood vessel network. However, such images are severely blurred by the strong scattering of body tissue, and it remains challenging for most models to accurately segment these blurred images. In addition, the convolution operation in the deep learning approach means that it extracts a mixture of blurred edges and clear centers, resulting in gradual distortion during upsampling. In this paper, we propose a novel and efficient deep learning model called TRC-Unet for segmenting blurred NIR images. The transformer connection (TRC) block extracts global spatial information from different scales by adaptively suppressing scattering and increasing the clarity of features. Our proposed transformer feature fusion (TFF) module closes the gap between the highly semantic feature maps of CNN and the adaptive fuzzy transformer output to enable a precise reconstruction of the segmentation. We evaluated TRC-Unet on both a simulated blurred DRIVE dataset and a NIR vessel dataset, and we achieved competitive results. (i.e., 83.86% Dice score on DRIVE and an average boost of 4.6% on simulated images at different depths).