Glaucoma is the second driving reason for partial or complete blindness among all the visual deficiencies which mainly occurs because of excessive pressure in the eye due to anxiety or depression which damages the optic nerve and creates complications in vision. Traditional glaucoma screening is a time-consuming process that necessitates the medical professionals' constant attention, and even so time to time due to the time constrains and pressure they fail to classify correctly that leads to wrong treatment. Numerous efforts have been made to automate the entire glaucoma classification procedure however, these existing models in general have a black box characteristics that prevents users from understanding the key reasons behind the prediction and thus medical practitioners generally can not rely on these system. In this article after comparing with various pre-trained models, we propose a transfer learning model that is able to classify Glaucoma with 94.71\% accuracy. In addition, we have utilized Local Interpretable Model-Agnostic Explanations(LIME) that introduces explainability in our system. This improvement enables medical professionals obtain important and comprehensive information that aid them in making judgments. It also lessen the opacity and fragility of the traditional deep learning models.