Mesh denoising (MD) is a critical task in geometry processing, as meshes from scanning or AIGC techniques are susceptible to noise contamination. The challenge of MD lies in the diverse nature of mesh facets in terms of geometric characteristics and noise distributions.Despite recent advancements in deep learning-based MD methods, existing MD networks typically neglect the consideration of geometric characteristics and noise distributions. In this paper, we propose Hyper-MD, a hyper-network-based approach that addresses this limitation by dynamically customizing denoising parameters for each facet based on its noise intensity and geometric characteristics. Specifically, Hyper-MD is composed of a hyper-network and an MD network. For each noisy facet, the hyper-network takes two angles as input to customize parameters for the MD network. These two angles are specially defined to reveal the noise intensity and geometric characteristics of the current facet, respectively. The MD network receives a facet patch as input, and outputs the denoised normal using the customized parameters. Experimental results on synthetic and real-scanned meshes demonstrate that Hyper-MD outperforms state-of-the-art mesh denoising methods.