Glaucoma is a highly perilous ocular disease that significantly impacts human visual acuity. This is a retinal condition that causes damage to the Optic Nerve Head (ONH) and can lead to permanent blindness if detected in a late stage. The prevention of permanent blindness is contingent upon the timely identification and intervention of glaucoma during its initial stages. This paper introduces a convolutional neural network (CNN) model that utilizes specific architectural designs to identify early-stage glaucoma by analyzing fundus images. This study utilizes publicly accessible datasets, including the Online Retinal Fundus Image Database for Glaucoma Analysis and Research (ORIGA), Structured Analysis of the Retina (STARE), and Retinal Fundus Glaucoma Challenge (REFUGE). The retinal fundus images are fed into AlexNet, VGG16, ResNet50, and InceptionV3 models for the purpose of classifying glaucoma. The ResNet50 and InceptionV3 models, both of which demonstrated a superior performance, were merged to create a hybrid model. The ORIGA dataset achieved high accuracy with an F1 Score of 97.4%, while the STARE dataset achieved higher accuracy with an F1 Score of 99.1%. The REFUGE dataset also showed excellent performance, with an F1 Score of 99.2%. The proposed methodology has established a reliable glaucoma diagnostic system, aiding ophthalmologists and physicians in conducting accurate mass screenings and diagnosing glaucoma. © 2024 Elsevier B.V., All rights reserved.