The exponential rise in technologies has revitalized academia-industries to achieve more efficient computer aided diagnosis systems. It becomes inevitable especially for Glaucoma detection which has been increasing with vast pace globally. Most of the existing approaches employs morphological features like optical disk and optical cup information, optical cup to disk ratio etc; however enabling optimal detection of such traits has always been challenge for researchers. On the other hand, in the last few years deep learning methods have gained widespread attention due to its ability to exploit fine grained features of images to make optimal classification decision. However, reliance of such methods predominantly depends on the presence of deep features demanding suitable feature extraction method. To achieve it major existing approaches extracts full-image features that with high dimensional kernel generates gigantically huge features, making classification computationally overburdened. Therefore, retaining optimal balance between deep features and computational overhead is of utmost significance for glaucoma detection and classification. With this motive, in this paper a novel hybrid deep learning model has been developed for Glaucoma detection and classification. The proposed Hybrid CNN model embodies Stacked Auto-Encoder (SAE) with transferable learning model AlexNet that extracts high dimensional features to make further two-class classification. To achieve computational efficiency, In addition to the classical ReLu and dropout (50%), we used Principle Component Analysis (PCA) and Linear Discriminant Analysis (LDA) algorithms. We applied 10-fold cross validation assisted Support Vector Machine classifier to perform two-class classification; Glaucomatous and Normal fundus images. Simulation results affirmed that the proposed Hybrid deep learning model with LDA feature selection and SVM-Poly classification achieves the maximum accuracy of 98.8%, precision 97.5%, recall 97.5% and F-Measure of 97.8%.