Magnetic resonance imaging (MRI) is a useful method for diagnosis of tumours in human brain. In this work, MRI images have been analysed to detect the regions containing tumour and classify these regions into three different tumour categories: meningioma, glioma, and pituitary. Deep learning is a relatively recent and powerful method for image classification tasks. Therefore, faster Region-based Convolutional Neural Networks (faster R-CNN), a deep learning method, has been utilized and implemented via TensorFlow library in this study. A publicly available dataset containing 3,064 MRI brain images (708 meningioma, 1426 glioma, 930 pituitary) of 233 patients has been used for training and testing of the classifier. It has been shown that faster R-CNN method can yield an accuracy of 91.66% which is higher than the related work using the same dataset.