The extensive use of medical CT has raised a public concern over the radiation dose to the patient. Reducing the radiation dose leads to increased CT image noise and artifacts, which can adversely affect not only the radiologists judgement but also the performance of downstream medical image analysis tasks. Various low-dose CT denoising methods, especially the recent deep learning based approaches, have produced impressive results. However, the existing denoising methods are all downstream-task-agnostic and neglect the diverse needs of the downstream applications. In this paper, we introduce a novel Task-Oriented Denoising Network (TOD-Net) with a task-oriented loss leveraging knowledge from the downstream tasks. Comprehensive empirical analysis shows that the task-oriented loss complements other task agnostic losses by steering the denoiser to enhance the image quality in the task related regions of interest. Such enhancement in turn brings general boosts on the performance of various methods for the downstream task. The presented work may shed light on the future development of context-aware image denoising methods.