Automatic and accurate classification of lesions in magnetic resonance imaging (MRI) are essential in early diagnosis and postoperative assessment of human brain tumor diseases. Clinically, neurologists and oncologists primarily diagnose brain tumor lesions within MRI images by scrutinizing their locations, signal characteristics, edge conditions, blood supply, and interactions with surrounding tissues. In this paper, we propose a novel joint-attention convolutional neural network (JACNN) tailored for brain tumor classification, in which tumor lesions within MRI images are extracted and incorporated within an efficient neural network to achieve superior classification accuracy. Specifically, we first introduce joint attention module (JAM) to generate fused feature map from the MRI image. This module is then seamlessly integrated into a concise streamlined classification network called BaseNet to form the proposed JACNN. Guided by the JAM, the proposed approach can leverage the information combined from global channel and local spatial region to further accelerate the training process and improve the brain tumor classification. Qualitative and quantitative experimental results compared with several state-of-the-art methods demonstrate the effectiveness and efficiency of proposed JACNN method in MRI brain tumor classification. The outcomes of this study will further facilitate the practical application of AI-driven MRI brain tumor classification.