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 natural language text as query. The relevance between the video and query is partial, mainly evident in two aspects: (1) Scope: The untrimmed video contains information-rich frames, and not all are relevant to the query. Strong correlation is typically observed only within the relevant moment, emphasizing the importance of capturing key content. (2) Modality: The relevance of query to different modalities varies; action descriptions align more with the visual elements, while character conversations are more related to textual information. Recognizing and addressing these modality-specific nuances is crucial for effective retrieval in VCMR. However, 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 distinct query representations tailored for different 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, followed by fusing multi-modal information for moment localization. Experimental results on TVR and DiDeMo datasets show that the proposed model outperforms the baselines, achieving a new state-of-the-art of VCMR.