Recent advancements in Large Language Models (LLMs) have driven growing interest in LLM-based agents for complex planning tasks. To avoid costly agent training, many studies adopted memory mechanism that enhances LLM with offline experiences or online trajectory analysis. However, existing works focus on single-granularity memory derived from dynamic environmental interactions, which are inherently constrained by the quality of the collected experiences. This limitation, in turn, constrain the diversity of knowledge and the flexibility of planning. We propose Coarse-to-Fine Grounded Memory (CFGM), a novel framework that grounds coarse-to-fine memories with LLM, thereby fully leverage them for flexible adaptation to diverse scenarios. CFGM grounds environmental information into coarse-grained focus points to guide experience collection in training tasks, followed by grounding of actionable hybrid-grained tips from each experience. At inference, CFGM retrieves task-relevant experiences and tips to support planning. When facing environmental anomalies, the LLM grounds the current situation into fine-grained key information, enabling flexible self-QA reflection and plan correction. Extensive experiments on AlfWorld, Webshop and ScienceWorld demonstrate that CFGM significantly outperforms competitive baselines and comprehensively optimizes memory-enhanced LLM Agent system.