Automatically narrating a video with natural language can assist people in grasping and managing massive videos on the Internet. From the perspective of video uploaders, they may have varied preferences for writing the desired video description to attract more potential followers, e.g. catching customers' attention for product videos. The Controllable Video Captioning task is therefore proposed to generate a description conditioned on the user demand and video content. However, existing works suffer from two shortcomings: 1) the control signal is fixed and can only express single-grained control; 2) the video description can not be further edited to meet dynamic user demands. In this paper, we propose a novel Video Description Editing (VDEdit) task to automatically revise an existing video description guided by flexible user requests. Inspired by human writing-revision habits, we design the user command as a {operation, position, attribute} triplet to cover multi-grained use requirements, which can express coarse-grained control (e.g. expand the description) as well as fine-grained control (e.g. add specified details in specified position) in a unified format. To facilitate the VDEdit task, we first automatically construct a large-scale benchmark dataset namely VATEX-EDIT in the open domain describing diverse human activities. Considering the real-life application scenario, we further manually collect an e-commerce benchmark dataset called EMMAD-EDIT. We propose a unified framework to convert the {operation, position, attribute} triplet into a textual control sequence to handle multi-grained editing commands. For VDEdit evaluation, we adopt comprehensive metrics to measure three aspects of model performance, including caption quality, caption-command consistency, and caption-video alignment.