Brain image classification is one of the most useful and widely needed processes in the medical system, and it is a highly challenging field. This paper presents a new method for selecting a significant subset of features as the input to the classifier, called mutual information-accelerated singular value decomposition (MI-ASVD). This novel algorithm is exploited to design an intelligent system for classifying MRI brain images into three classes: healthy, high-grade glioma, and low-grade glioma. The proposed system has six stages: pre-processing, clustering, tumour localization, feature extraction, MI-ASVD and classification. First, the MR images are smoothed by using enhancement techniques such as Gaussian kernel filters. Then, local difference in intensity-means (LDI-Means) clustering is employed to segment and detect suspicious regions. The grey-level run-length matrix (GLRLM), texture, and colour intensity features are used for tumour feature extraction. Later, a special method including a summation of feature selection and dimensionality reduction, MI-ASVD, is applied to select the most useful features for the classification process. Finally, the simplified residual neural network technique is implemented to classify the MR brain images. Using MI-ASVD provided accurate and more efficacious results in classification compared with the original feature space and with two other standard dimensionality reduction methods, principal component analysis (PCA) and singular value decomposition (SVD). It achieved a classification accuracy of 94.91 & x0025;, which is better than the two state-of-the-art techniques as well as methods from similar published studies.