Prompt engineering, as an efficient and effective way to leverage Large Language Models (LLM), has drawn a lot of attention from the research community. The existing research primarily emphasizes the importance of adapting prompts to specific tasks, rather than specific LLMs. However, a good prompt is not solely defined by its wording, but also binds to the nature of the LLM in question. In this work, we first quantitatively demonstrate that different prompts should be adapted to different LLMs to enhance their capabilities across various downstream tasks in NLP. Then we novelly propose a model-adaptive prompt optimizer (MAPO) method that optimizes the original prompts for each specific LLM in downstream tasks. Extensive experiments indicate that the proposed method can effectively refine prompts for an LLM, leading to significant improvements over various downstream tasks.