Optic disc (OD) and cup (OC) regions depicted on color fundus images are important landmarks for assessing glaucoma. In this study, we developed a novel and general distance-guided deep learning strategy (DGLS) to simultaneously segment the OD and OC from color fundus images based on an available network (i.e., U-Net). The developed method used two different types of annotation regions to characterize each target object and then converted the regions into location information leveraging a distance transform in a coarse-to-fine segmentation framework. We validated the developed algorithm by applying it to simultaneously segment OD and OC from color fundus images. Experiments on four public datasets (i.e., the REFUGE, BinRushed, DirshtiGS, and Magrabia datasets) suggested that the developed DGLS achieved, on average, a Dice Score (DS) of 0.9047, a Jaccard index (JI) of 0.8387, and a Hausdorff distance (HD, in pixel) of 2.6211 for the OD and OC in the coarse segmentation stage, and 0.9065, 0.8416, and 2.5930 in the fine segmentation stage. This algorithm demonstrated a superior performance compared to the U-Net and its several variants (i.e., Attention U-Net, BiO-Net and asymmetric network) trained on a single annotation and the traditional training strategy.