Deep neural networks have recently achieved a great success in neural video compression (NVC), but face big challenges in low-latency scenarios for its high computational complexity. Quantization is an effective way to reduce memory footprint and computational complexity of NVC methods. However, existing methods overlook the unique characteristics of video frames and typically employ a fixed bit-width approach. In this paper, we propose a ROI(Region of Interest)-aware dynamic quantization method for NVC, by analyzing ROIs within video frames and dynamically altering the quantization strategy. To achieve a better frame reconstruction with lower computational complexity, our method allocates higher bit-widths for critical regions and lower bit-widths for less crucial areas. We design an efficient bit-allocator that adaptively determines quantization levels across different regions and frames, guided by the motion and texture complexity of the region. Experimental results on standard test videos demonstrate effectiveness of the proposed dynamic quantization method.