The paper introduces a novel and efficient method of automated glaucoma detection from fundus images using a hyper-parameter-tuned Evolutionary Convolutional Neural Network (ECNN). The novel model applies a hybrid optimizer—Gazelle Optimization Algorithm (GOA) and Chimp Optimization Algorithm (COA)—with a focus on enhancing the rate of convergence and classification accuracy. The fundus images are preprocessed using a Gaussian morphological filter for contrast enhancement and resolution. Significant texture features are extracted from the Gray-Level Co-occurrence Matrices (GLCM), which are subsequently input to the ECNN for classification. The hybrid GOA-COA approach greatly enhances the process of optimization with a best fitness value of 0.973 in iteration 20 for outperforming conventional optimizers like GOA, COA, and RCGA both in convergence rate and best fitness value. Experimental results show that the proposed GOA-COA-ECNN model has an accuracy of 98.4%, an F-measure of 0.968, and a precision of 0.980. Moreover, the system carries out the detection in only 2.1 s, thus making it highly appropriate for real-time clinical screening.