Video Corpus Moment Retrieval (VCMR) is a new video retrieval task aimed at retrieving a relevant moment from a large corpus of untrimmed videos using a text query. The relevance between the video and query is partial, mainly evident in two aspects:~(1)~Scope: The untrimmed video contains many frames, but not all are relevant to the query. Strong relevance is typically observed only within the relevant moment.~(2)~Modality: The relevance of the query varies with different modalities. Action descriptions align more with visual elements, while character conversations are more related to textual information.Existing methods often treat all video contents equally, leading to sub-optimal moment retrieval. We argue that effectively capturing the partial relevance between the query and video is essential for the VCMR task. To this end, we propose a Partial Relevance Enhanced Model~(PREM) to improve VCMR. VCMR involves two sub-tasks: video retrieval and moment localization. To align with their distinct objectives, we implement specialized partial relevance enhancement strategies. For video retrieval, we introduce a multi-modal collaborative video retriever, generating different query representations for the two modalities by modality-specific pooling, ensuring a more effective match. For moment localization, we propose the focus-then-fuse moment localizer, utilizing modality-specific gates to capture essential content. We also introduce relevant content-enhanced training methods for both retriever and localizer to enhance the ability of model to capture relevant content. Experimental results on TVR and DiDeMo datasets show that the proposed model outperforms the baselines, achieving a new state-of-the-art of VCMR. The code is available at \url{https://github.com/hdy007007/PREM}.