Recent advancements in diffusion models have significantly improved video generation and editing capabilities. However, multi-grained video editing, which encompasses class-level, instance-level, and part-level modifications, remains a formidable challenge. The major difficulties in multi-grained editing include semantic misalignment of text-to-region control and feature coupling within the diffusion model. To address these difficulties, we present VideoGrain, a zero-shot approach that modulates space-time (cross- and self-) attention mechanisms to achieve fine-grained control over video content. We enhance text-to-region control by amplifying each local prompt's attention to its corresponding spatial-disentangled region while minimizing interactions with irrelevant areas in cross-attention. Additionally, we improve feature separation by increasing intra-region awareness and reducing inter-region interference in self-attention. Extensive experiments demonstrate our method achieves state-of-the-art performance in real-world scenarios. Our code, data, and demos are available on the project page.