The accurate prediction of glioma grade before surgery is essential for treatment planning and prognosis. Since the gold standard (i.e., biopsy)for grading gliomas is both highly invasive and expensive, and there is a need for a noninvasive and accurate method. In this study, we proposed a novel radiomics-based pipeline by incorporating the intratumoral and peritumoral features extracted from preoperative mpMRI scans to accurately and noninvasively predict glioma grade. To address the unclear peritumoral boundary, we designed an algorithm to capture the peritumoral region with a specified radius. The mpMRI scans of 285 patients derived from a multi-institutional study were adopted. A total of 2153 radiomic features were calculated separately from intratumoral volumes (ITVs)and peritumoral volumes (PTVs)on mpMRI scans, and then refined using LASSO and mRMR feature ranking methods. The top-ranking radiomic features were entered into the classifiers to build radiomic signatures for predicting glioma grade. The prediction performance was evaluated with five-fold cross-validation on a patient-level split. The radiomic signatures utilizing the features of ITV and PTV both show a high accuracy in predicting glioma grade, with AUCs reaching 0.968. By incorporating the features of ITV and PTV, the AUC of IPTV radiomic signature can be increased to 0.975, which outperforms the state-of-the-art methods. Additionally, our proposed method was further demonstrated to have strong generalization performance in an external validation dataset with 65 patients. The source code of our implementation is made publicly available at https://github.com/chengjianhong/glioma_grading.git.