Retinal fundus images are widely used to diagnose retinal diseases and can potentially be used for early diagnosis and prevention of chronic vascular diseases and diabetes. While various automatic retinal vessel segmentation methods using deep learning have been proposed, they are mostly based on common CNN structures developed for other tasks such as classification.We present a novel and simple multi-scale convolutional neural network (CNN) structure for retinal vessel segmentation. We first provide a theoretical analysis of existing multi-scale structures based on signal processing. In previous structures, multi-scale representations are achieved through downsampling by subsampling and decimation. By incorporating scale-space theory, we propose a simple yet effective multi-scale structure for CNNs using upsampling, which we term scale-space approximated CNN (SSANet). Based on further analysis of the effects of the SSA structure within a CNN, we also incorporate residual blocks, resulting in a multi-scale CNN that outperforms current state-of-the-art methods.Quantitative evaluations are presented as the area-under-curve (AUC) of the receiver operating characteristic (ROC) curve and the precision-recall curve, as well as accuracy, for four publicly available datasets, namely DRIVE, STARE, CHASE_DB1, and HRF. For the CHASE_DB1 set, the SSANet achieves state-of-the-art AUC value of 0.9916 for the ROC curve. An ablative analysis is presented to analyze the contribution of different components of the SSANet to the performance improvement.The proposed retinal SSANet achieves state-of-the-art or comparable accuracy across publicly available datasets, especially improving segmentation for thin vessels, vessel junctions, and central vessel reflexes.