Glaucoma is a major contributor to irreversible blindness, a condition marked caused by optic nerve injury, which is frequently brought on by high intraocular pressure. For vision loss to be effectively managed and prevented, early detection is essential. Conventional diagnostic techniques mostly rely on labor-intensive, error-prone manual analysis. To overcome these challenges, a novel deep learning based GD2-EffiNet model is proposed for the detecting of Glaucoma disease. Initially, images are pre-processed using the Gaussian Star Filter (GaSF) to enhance image quality and remove noise. EfficientNet-B0 is employed to extract deep features, enabling the classification of normal and abnormal glaucoma images. Finally, UNet is used to segment the abnormal regions, facilitating early diagnosis. The effectiveness of the proposed GD2-EffiNet method using metrics like F1 score, sensitivity, accuracy, and specificity. The classification accuracy of the proposed GD2-EffiNet model was 99.41%. The proposed model enhanced the total accuracy 0.03%, 1.56%, and 0.59% better than CG-EffiNet, ODGNet, SEG-UNet respectively. The proposed GD2-EffiNet model offers a reliable and efficient solution for automated Glaucoma disease detection, which is essential for early diagnosis and effective management of the condition.