This paper presents LUVS-Net, which is a lightweight convolutional network for retinal vessel segmentation in fundus images that is designed for resource-constrained devices that are typically unable to meet the computational requirements of large neural networks. The computational challenges arise due to low-quality retinal images, wide variance in image acquisition conditions and disparities in intensity. Consequently, the training of existing segmentation methods requires a multitude of trainable parameters for the training of networks, resulting in computational complexity. The proposed Lightweight U-Net for Vessel Segmentation Network (LUVS-Net) can achieve high segmentation performance with only a few trainable parameters. This network uses an encoder–decoder framework in which edge data are transposed from the first layers of the encoder to the last layer of the decoder, massively improving the convergence latency. Additionally, LUVS-Net’s design allows for a dual-stream information flow both inside as well as outside of the encoder–decoder pair. The network width is enhanced using group convolutions, which allow the network to learn a larger number of low- and intermediate-level features. Spatial information loss is minimized using skip connections, and class imbalances are mitigated using dice loss for pixel-wise classification. The performance of the proposed network is evaluated on the publicly available retinal blood vessel datasets DRIVE, CHASE_DB1 and STARE. LUVS-Net proves to be quite competitive, outperforming alternative state-of-the-art segmentation methods and achieving comparable accuracy using trainable parameters that are reduced by two to three orders of magnitude compared with those of comparative state-of-the-art methods.