Image denoising via machine learning techniques, particularly neural networks, has been shown to achieve state-of-the-art performance. However, in practice security and privacy issues undesirably arise in applying a trained machine learning model to image denoising. In this paper, we propose a system framework that enables the owner of a trained machine learning model to provide secure image denoising service to an authorized user, via the aid of cloud computing. Our framework ensures that the cloud server learns nothing about the model and the user's images, while the user learns nothing about the model except denoised images. Experiments are conducted for performance evaluation, and the results show that our design can achieve denoising quality close to that in the plaintext domain. For future work, we plan to explore various directions for optimizing the runtime performance.