A definitive diagnosis of a brain tumour is essential for enhancing treatment success and patient survival. However, it is difficult to manually evaluate multiple magnetic resonance imaging (MRI) images generated in a clinic. Therefore, more precise computer-based tumour detection methods are required. In recent years, many efforts have investigated classical machine learning methods to automate this process. Deep learning techniques have recently sparked interest as a means of diagnosing brain tumours more accurately and robustly. The goal of this study, therefore, is to employ brain MRI images to distinguish between healthy and unhealthy patients (including tumour tissues). As a result, an enhanced convolutional neural network is developed in this paper for accurate brain image classification. The enhanced convolutional neural network structure is composed of components for feature extraction and optimal classification. Nonlinear Lévy Chaotic Moth Flame Optimizer (NLCMFO) optimizes hyperparameters for training convolutional neural network layers. Using the BRATS 2015 data set and brain image datasets from Harvard Medical School, the proposed model is assessed and compared with various optimization techniques. The optimized CNN model outperforms other models from the literature by providing 97.4% accuracy, 96.0% sensitivity, 98.6% specificity, 98.4% precision, and 96.6% F1-score, (the mean of the weighted harmonic value of CNN precision and recall).