Glaucoma disease (GD) is a rapidly growing consequence of Glaucoma estimates globally. The importance of accurate GD diagnosis in improving patient care and treatment outcomes has seen a significant increase in research interest in recent years. The significant advancement in Deep Learning (DL) approaches has proven to be superior to traditional detection methods. In this paper, we proposed a Deep Learning constructed using a convolutional neural network (CNN) for the automated detection of glaucoma from fundus images to distinguish between Glaucoma -affected and healthy. The important features from the input data are extracted using a CNN that has been built and trained to do so. On the ACRIMA dataset, these frameworks have been tested and trained, which contains a total of 705 images. We also evaluated how well our proposed CNN-based system performed compared to those other pretrained models (EfficientNetB0, ResNet101, Resnet50, VGG16, and InceptionV3). The aim of this paper is to comparative analysis of the performance obtained from different configurations with CNN architectures and hyper-parameter tuning. Among the considered deep learning models, the EfficientNetB0 model showed the highest accuracy of 98% for the ACRIMA fundus image dataset. We accomplished the best performance using our proposed CNN network, achieving 98.1% accuracy, 98.31% sensitivity, and 97.85% specificity for the ACRIMA dataset. Additionally, this study presents a comparative analysis of how changes in the hyperparameter of the model can affect classification performances. As a result, the proposed method is more efficient and robust compared to that described in the literature.