Although deep learning has significantly advanced MRI-based brain tumor classification, computational feasibility for clinical deployment remains bottlenecked by the heavy parameter cost of Vision Transformers and the limited global context awareness of Convolutional Neural Networks. We propose HCViT (Hybrid Convolutional Vision Transformer), a novel architecture designed for medical imaging by integrating local feature extraction (ConvStem), global context modeling (Transformer), and spatially-aware attention via learnable convolutional bias (ConvBias). This domain-aware hybridization preserves anatomical details while capturing long-range dependencies, overcoming key limitations of pure CNNs and Transformers. Evaluated on binary brain MRI classification (tumor vs. no tumor), HCViT achieves 96.25% validation accuracy, matching Hybrid ViT (ResNet26d + ViT), the top baseline, while being 7× more parameter-efficient (8.99M vs 62.78M) and 2.5× more computationally efficient (2.012 vs 5.049 GFLOPs). It surpasses ResNet-50 (93.75%), ConvNeXt-Tiny (92.50%), ViT-Tiny (83.75%), ViT-Base (68.75%), and Swin-T (78.75%). With 2032 img/s inference throughput (batch=32), HCViT offers clinically viable speed without compromising diagnostic precision. Its robust generalization and high sensitivity to subtle lesions make it suitable for real-world deployment, including resource-limited or high-throughput clinical settings. This work demonstrates that domain-informed architectural design, not merely adopting trending models, is essential for effective, efficient, and interpretable medical AI. HCViT establishes a new state-of-the-art efficiency-accuracy trade-off for brain tumor classification and provides a scalable foundation for future extensions: multi-class diagnosis, integration with segmentation models, and edge-device deployment. By bridging CNNs’ local inductive bias with Transformers’ global modeling, enhanced by spatial attention, HCViT sets a benchmark for next-generation medical vision models.