This paper presents the novel smart hybrid EfficientNet-deep autoencoder (EF-DA) Deep Neural Network model to classify brain images. This is the succession of modified EfficientNetB0 with a deep autoencoder to detect tumours. Initially, the feature extraction is done by modified EfficientNet, and then classification is done by the proposed smart deep autoencoder. The images are filtered, cropped by morphological operations, and augmented to train a deep hybrid EF-DA model in the first stage. In the second stage, a modified deep autoencoder is used for classification. The statistical result analysis of the hybrid model is assessed using seven types of degree metrics like F-score, precision, recall, specificity, Kappa score, accuracy, and area under the ROC curve (AUC) score. It is compared with three types of pre-trained models like MobileNet, MobileNetV2, and ResNet50 for analysis. The EF-DA model has achieved an overall accuracy of 99.34% and an AUC score of 99.95%.