Adding proper background music helps complete a short video to be shared. Towards automating the task, previous research focuses on video-to-music retrieval (VMR), aiming to find amidst a collection of music the one best matching the content of a given video. Since music tracks are typically much longer than short videos, meaning the returned music has to be cut to a shorter moment, there is a clear gap between the practical need and VMR. In order to bridge the gap, we propose in this paper video to music moment retrieval (VMMR) as a new task. To tackle the new task, we build a comprehensive dataset Ad-Moment which contains 50K short videos annotated with music moments and develop a two-stage approach. In particular, given a test video, the most similar music is retrieved from a given collection. Then, a Transformer based music moment localization is performed. We term this approach Retrieval and Localization (ReaL). Extensive experiments on real-world datasets verify the effectiveness of the proposed method for VMMR.