Early detection and diagnosis of brain tumors are essential for early intervention and eventually successful treatment plans leading to either a full recovery or an increase in the patient lifespan. However, diagnosis of brain tumors is not an easy task since it requires highly skilled professionals, making this procedure both costly and time-consuming. The diagnosis process relying on MR images gets even harder in the presence of similar objects in terms of their density, size, and shape. No matter how skilled professionals are, their task is still prone to human error. The main aim of this work is to propose a system that can automatically classify and diagnose glioma brain tumors into one of the four tumor types: (1) necrosis, (2) edema, (3) enhancing, and (4) non-enhancing. In this paper, we propose a combined texture discrete wavelet transform (DWT) and statistical features based on the first- and second-order features for the accurate classification and diagnosis of multiclass glioma tumors. Four well-known classifiers, namely, support vector machines (SVM), random forest (RF), multilayer perceptron (MLP), and naïve Bayes (NB), are used for classification. The BraTS 2018 dataset is used for the experiments, and with the combined DWT and statistical features, the RF classifier achieved the highest average accuracy whether for separated modalities or combined modalities. The highest average accuracy of 89.59% and 90.28% for HGG and LGG, respectively, was reported in this paper. It has also been observed that the proposed method outperforms similar existing methods reported in the extant literature.