Medical image analysis is a field where the classification of brain tumors is essential to allow proper diagnosis and treatment plan. This study suggests an effective mechanism of classifying brain MRI images into glioma, meningioma, pituitary and non-tumor images by combining deep learning and machine learning techniques. This model uses the AlexNet framework to extract deep features, Principal Component Analysis (PCA) to reduce dimensionalities and ReliefF to select features. To identify the best model, the chosen features are tested with the help of different supervised classifiers, such as Support Vector machine (SVM), K-Nearest Neighbor (KNN), Random Forest, and Naive Bayes. The proposed hybrid framework is evaluated on publicly available dataset. Optimal performance is obtained with the SVM classifier, with an accuracy of 94.36 percent and F1-score of 0.94, as the proposed approach is effective in improving the feature discriminability whilst incurring less computation.