Blood vessel segmentation is an essential element of automatic retinal disease screening systems. In particular, retinal blood vessel analysis from fundus image is vital in the identification and diagnosis of cardiovascular and ophthalmological diseases (Ex: Diabetic Retinopathy, Macular degeneration, Retinal Pigmentosa, Macular Edema, and various stages of Glaucoma, etc). Wherefore, the diagnosis of these diseases by automatic vessel segmentation has become essential, especially in disclosure of premature prognosis of vision condition. In general, blood vessel extraction is divided into vessel tracking and pixel classification. In vessel tracking a vasculature model is expanded from a seed point. In pixel classification, the classifier classifies the pixels as either a vessel or background pixel, which is demonstrated in the proposed architecture. In this paper, deep learning based 19 layer U-Net architecture is proposed for the accurate and efficient segmentation of blood vessels. Prior to segmentation, a pre-processing block of AlexNet architecture is introduced for the classification of high-quality images from the experimented databases. This pre-classification stage helps in efficiently picking high-quality images determined by clarity, field definition, and sharpness. AlexNet classification is pivotal in enhancing the overall performance of the system by segmenting fine and tiny blood vessels. The proposed U-Net architecture has an encoder-decoder framework with 9 and 5 convolutional layers in each respectively. In order to boost the efficiency of the network as well as to reduce training and testing time, a proper choice of kernel dimension and number of filters are necessary. Our architecture was investigated on popular databases such as DRIVE, ARIA_d and MESSIDOR and various performance measures (accuracy, sensitivity, specificity, sensibility, Dice coefficient, and Jaccard coefficient) have been computed along with the Receiver Operating Characteristics. It is observed that the accuracy for DRIVE, ARIA_d and MESSIDOR are 90.60%, 87.60% and 83.42%, respectively. Area under curve in Receiver Operating Characteristics plot is found to be 98.54%, 93.28% and 88.18%, for DRIVE, ARIA_d and MESSIDOR databases, respectively. Results with the proposed architecture show remarkable improvement in the performance metrics for blood vessel segmentation.