Glaucoma is a condition that causes permanent damage to the optic nerves, resulting in partial or total vision loss. In this paper, a deep learning model using Tripartite Tier Convolutional Neural Network (TTCNN) structure is proposed to detect the glaucomatous images from the normal images. The proposed system includes different steps such as preprocessing, attribute extraction, and glaucoma evaluation. Preprocessing discusses how to convert RGB fundus images to grayscale and how to improve fundus feature contrast. Then, the optic cup (OC) and optic disc (OD) boundaries are fragmented during the attribute extraction using TTCNN. Finally, the Cup-to-Disc Ratio (CDR) has been determined to diagnose glaucoma in the image. This system has been verified on two different publicly available datasets DRIVE and RIM-ONE, yielding an average sensitivity, specificity, accuracy, and precision in glaucoma diagnosis of 84.50%, 98.01%, 99%, and 84% respectively. The obtained results show that the proposed recognition system is suitable for detecting glaucoma with higher precision.