Image classification is one of the typical computational applications widely used in the medical field, especially for abnormality detection in magnetic resonance (MR) brain images. Medical image classification is a pattern recognition technique in which different images are categorized into several groups based on some similarity measures. One of the significant applications is the tumor type identification in abnormal MR brain images. The proposed multi-class brain tumor classification system comprises feature extraction and classification. In feature extraction, the attributes of the co-occurrence matrix and the histogram are represented within the feature vector. In this work, the advantage of both co-occurrence matrix and histogram to extract the texture feature from every segment is used for better classification. In classification, the fuzzy logic-based hybrid kernel is designed and applied to train the support vector machine for automatic classification of four different types of brain tumors such as Meningioma, Glioma, Astrocytoma, and Metastases. Based on the experimental results, the proposed brain tumor classification method is more robust than other traditional methods in terms of the evaluation metrics, sensitivity, specificity, and accuracy.