Glaucoma, an eye disease, occurs due to Retinal damages and it is an ordinary cause of blindness. Most of the available examining procedures are too long and require manual instructions to use them. In this work, we proposed a multi-level deep convolutional neural network (ML-DCNN) architecture on retinal fundus images to diagnose glaucoma. We collected a retinal fundus images database from the local hospital. The fundus images are pre-processed by an adaptive histogram equalizer to reduce the noise of images. The ML-DCNN architecture is used for features extraction and classification into two phases, one for glaucoma detection known as detection-net and the second one is classification-net used for classification of affected retinal glaucoma images into three different categories: Advanced, Moderate and Early. The proposed model is tested on 1338 retinal glaucoma images and performance is measured in the form of different statistical terms known as sensitivity (SE), specificity (SP), accuracy (ACC), and precision (PRE). On average, SE of 97.04%, SP of 98.99%, ACC of 99.39%, and PRC of 98.2% are achieved. The obtained outcomes are comparable to the state-of-the-art systems and achieved competitive results to solve the glaucoma eye disease problems for complex glaucoma eye disease cases.