In this paper, we propose BeamLLM, a vision-aided millimeter-wave (mmWave) beam prediction framework leveraging large language models (LLMs) to address the challenges of high training overhead and latency in mmWave communication systems. By combining computer vision (CV) with LLMs' cross-modal reasoning capabilities, the framework extracts user equipment (UE) positional features from RGB images and aligns visual-temporal features with LLMs' semantic space through reprogramming techniques. Evaluated on a realistic vehicle-to-infrastructure (V2I) scenario, the proposed method achieves 61.01% top-1 accuracy and 97.39% top-3 accuracy in standard prediction tasks, significantly outperforming traditional deep learning models. In few-shot prediction scenarios, the performance degradation is limited to 12.56% (top-1) and 5.55% (top-3) from time sample 1 to 10, demonstrating superior prediction capability.