A brain-computer interface (BCI) system enables direct communication between the brain and external devices, offering significant potential for assistive technologies and advanced human-computer interaction. Despite progress, BCI systems face persistent challenges, including signal variability, classification inefficiency, and difficulty adapting to individual users in real time. In this study, we propose a novel hybrid quantum learning model, termed QSVM-QNN, which integrates a Quantum Support Vector Machine (QSVM) with a Quantum Neural Network (QNN), to improve classification accuracy and robustness in EEG-based BCI tasks. Unlike existing models, QSVM-QNN combines the decision boundary capabilities of QSVM with the expressive learning power of QNN, leading to superior generalization performance. The proposed model is evaluated on two benchmark EEG datasets, achieving high accuracies of 0.990 and 0.950, outperforming both classical and standalone quantum models. To demonstrate real-world viability, we further validated the robustness of QNN, QSVM, and QSVM-QNN against six realistic quantum noise models, including bit flip and phase damping. These experiments reveal that QSVM-QNN maintains stable performance under noisy conditions, establishing its applicability for deployment in practical, noisy quantum environments. Beyond BCI, the proposed hybrid quantum architecture is generalizable to other biomedical and time-series classification tasks, offering a scalable and noise-resilient solution for next-generation neurotechnological systems.