One of the leading reasons globally of cancer-related deaths is brain tumors. The classification of brain tumors is a challenging research issue. Concerning intensity, size, and shape, brain tumors show high variations. Tumors can display similar appearances from different pathological types. To classify and diagnose brain tumors, there are several imaging techniques utilized. Fortunately, because of its prior quality of image, and also the reality of depending on no ionizing radiation, Magnetic Resonance Imaging (MRI) is generally used. With recent developments in deep learning, artificial intelligence (AI) methods can assist radiologists in understanding medical images rapidly. This paper proposes a brain tumor classification method that employs a deep transfer learning method with a new fine-tuning strategy and a Support Vector Machine (SVM) as a classifier. First, preprocessing is applied to MRI images. Second, the data augmentation technique is applied with resampling to increase the dataset size. Then, the extracted features are from a pre-trained custom Convolutional Neural Network (CNN) model and the ResNet-50 method by using deep Transfer Learning (TL). Generally, after the convolution layers, features are flattened and directly given to SVM for classification. On the other hand, this work applied a new fine-tuning of the parameters for transfer learning. In particular, dense layers with dropout and Rectified Linear Units (ReLU) are applied after flattening. Then, the output of the final dense layer is given to SVM for classification. The efficiency of the proposed transfer learning-based classification approach using different settings is tested on the Figshare dataset which includes the three sorts of MRI brain tumors; meningioma, glioma, and pituitary. Results show that the proposed deep transfer learning approach is adequate; transfer learning using the proposed CNN architecture with fine-tuning and SVM classifier achieves 99.35% accuracy, whereas transfer learning that use ResNet-50 with fine-tuning of parameters yields a classification accuracy of 99.61%. The results of the proposed approach are very promising compared to state-of-the-art on the Figshare dataset.