Video Large Language Models (Video-LLMs) have demonstrated remarkable capabilities in coarse-grained video understanding, however, they struggle with fine-grained temporal grounding. In this paper, we introduce Grounded-VideoLLM, a novel Video-LLM adept at perceiving and reasoning over specific video moments in a fine-grained manner. We identify that current Video-LLMs have limitations for fine-grained video understanding since they lack effective temporal modeling and timestamp representation. In light of this, we sharpen our model by incorporating (1) an additional temporal stream to encode the relationships between frames and (2) discrete temporal tokens enriched with specific time knowledge to represent timestamps. To optimize the training of Grounded-VideoLLM, we employ a multi-stage training scheme, beginning with simple video-captioning tasks and progressively introducing video temporal grounding tasks of increasing complexity. To further enhance Grounded-VideoLLM's temporal reasoning capability, we also curate a grounded VideoQA dataset by an automatic annotation pipeline. Extensive experiments demonstrate that Grounded-VideoLLM not only excels in fine-grained grounding tasks such as temporal sentence grounding, dense video captioning, and grounded VideoQA, but also shows great potential as a versatile video assistant for general video understanding.