Ophthalmologists use the optic disc to cup ratio as one factor to diagnose glaucoma. Optic disc in fundus images is the area where blood vessels and optic nerve fibers enter the retina. A cup to disc ratio (the diameter of the cup divided by the diameter of the optic disc) greater than 0.3 is considered to be suggestive of glaucoma. Therefore, we are developing automatic methods to estimate optic disc and cup areas, and the optic disc to cup ratio. There are four steps to estimate the ratio: region of interest (ROI) area detection (where optic disc is in the center) from the fundus image, optic disc segmentation from the ROI, cup segmentation from the optic disc area, and cup to optic disc ratio estimation. This paper proposes an automated method to segment the optic disc from the ROI using deep learning. A Fully Convolutional Network (FCN) with a U-Net architecture is used for the segmentation. We use fundus images from MESSIDOR dataset in this experiment, a public dataset containing 1,200 fundus images. We divide the dataset into five equal subsets for training and independent testing (each set has four subsets for training and one subset for testing). The proposed method outperforms other existing algorithms. The results show 0.94 Jaccard index, 0.98 sensitivity, 0.99 specificity, and 0.99 accuracy.