The vascular structure of blood vessels is important in diagnosing retinal conditions such as glaucoma and diabetic retinopathy. Accurate segmentation of these vessels can help in detecting retinal objects such as the optic disc and optic cup and hence determine if there are damages to these areas. Moreover, the structure of the vessels can help in diagnosing glaucoma. The rapid development of digital imaging and computer-vision techniques has increased the potential for developing approaches for segmenting retinal vessels. In this paper, we propose an approach for segmenting retinal vessels that uses deep learning along with transfer learning. We adapted the U-Net structure to use a customized InceptionV3 as the encoder and used multiple skip connections to form the decoder. Moreover, we used a weighted loss function to handle the issue of class imbalance in retinal images. Furthermore, we contributed a new dataset to this field. We tested our approach on six publicly available datasets and a newly created dataset. We achieved an average accuracy of 95.60\% and a Dice coefficient of 80.98\%. The results obtained from comprehensive experiments demonstrate the robustness of our approach to the segmentation of blood vessels in retinal images obtained from different sources. Our approach results in greater segmentation accuracy than other approaches.