Medical image classification is the process of separating data into a specified number of classes. In recent years, Magnetic Resonance Imaging (MRI) has been widely used in the detection and diagnosis of brain tumors. In this study, it was aimed to classify three different brain tumors (glioma, meningioma and pituitary) using convolutional neural network (CNN) on T1-weighted MR images and to determine the efficiency of axial, coronal and sagittal MR planes in classification. The weights were initialized by transferring to CNN from DenseNet121 network, which was previously trained with ImageNet dataset. In addition, data augmentation was performed on MR images using affine and pixel-level transformations. The features obtained from the first fully connected layer of the trained CNN were also classified by support vector machine (SVM), k nearest neighbor (kNN), and Bayes methods. The performances of these classifiers were measured by the sensitivity, specificity, accuracy, area under curve, and the Pearson correlation coefficient on the test dataset. The accuracy values of the developed CNN and CNN-based SVM, kNN, and Bayes classifiers are 0.9860, 0.9979, 0.9907, and 0.8933, respectively. The CNN-based SVM model proposed for brain tumor classification obtained higher performance values than similar studies in the literature. In addition, coronal plane of the brain was found to give better results than other planes in determining the tumor type.