Background: Diagnosing brain tumours remains a challenging task in clinical practice. Despite their questionable accuracy, magnetic resonance image (MRI) scans are presently considered the optimal facility for assessing the growth of tumours. However, the efficiency of manual diagnosis is low, and high computational cost and poor convergence restrict the application of machine learning methods. This study aims to design a method that can reliably diagnose brain tumours from MRI scans. Methods: First, image pre-processing (which includes background removal, size standardization, noise removal, and contrast enhancement) is utilized to normalize the images. Then, grey level co-occurrence matrix features are selected as texture features of the brain MRI scans. Finally, a method combining a back propagation neural network (BPNN) and an extended set-membership filter (ESMF) is proposed to classify features and perform image classification. Results: A total of 304 patient MRI series (247 images of brains with tumours and 57 images of normal brains) were included and assessed in this study. The results revealed that our proposed method can achieve an accuracy of 95.40% and has classification accuracies of 97.14% and 88.24% for brain tumour and normal brain, respectively. Conclusion: This study proposes an automatic brain tumour detection model constructed using a combination of BPNN and ESMF. The model is found to be able to accurately classify brain MRI scans as normal or tumour images.