Deep learning (DL) networks have shown attractive performance in medical image processing tasks such as brain tumor classification. However, they are often criticized as mysterious "black boxes". The opaqueness of the model and the reasoning process make it difficult for health workers to decide whether to trust the prediction outcomes. In this study, we develop an interpretable multi-part attention network (IMPA-Net) for brain tumor classification to enhance the interpretability and trustworthiness of classification outcomes. The proposed model not only predicts the tumor grade but also provides a global explanation for the model interpretability and a local explanation as justification for the proffered prediction. Global explanation is represented as a group of feature patterns that the model learns to distinguish high-grade glioma (HGG) and low-grade glioma (LGG) classes. Local explanation interprets the reasoning process of an individual prediction by calculating the similarity between the prototypical parts of the image and a group of pre-learned task-related features. Experiments conducted on the BraTS2017 dataset demonstrate that IMPA-Net is a verifiable model for the classification task. A percentage of 86% of feature patterns were assessed by two radiologists to be valid for representing task-relevant medical features. The model shows a classification accuracy of 92.12%, of which 81.17% were evaluated as trustworthy based on local explanations. Our interpretable model is a trustworthy model that can be used for decision aids for glioma classification. Compared with black-box CNNs, it allows health workers and patients to understand the reasoning process and trust the prediction outcomes.