Segmenting of clinically important retinal blood vessels into arteries and veins is a prerequisite for retinal vessel analysis. Such analysis can provide potential insights and bio-markers for identifying and diagnosing various retinal eye diseases. Alteration in the regularity and width of the retinal blood vessels can act as an indicator of the health of the vasculature system all over the body. It can help identify patients at high risk of developing vasculature diseases like stroke and myocardial infarction. Over the years, various Deep Learning architectures have been proposed to perform retinal vessel segmentation. Recently, attention mechanisms have been increasingly used in image segmentation tasks. The work proposes a new Deep Learning approach for artery-vein segmentation. The new approach is based on the Attention mechanism that is incorporated into the WNet Deep Learning model, and we call the model as Attention-WNet. The proposed approach has been tested on publicly available datasets such as HRF and DRIVE datasets. The proposed approach has outperformed other state-of-art models available in the literature.