Catastrophic Forgetting (CF) means models forgetting previously acquired knowledge when learning new data. It compromises the effectiveness of large language models (LLMs) during fine-tuning, yet the underlying causes have not been thoroughly investigated. This paper takes the first step to reveal the direct link between the flatness of the model loss landscape and the extent of CF in the field of LLMs. Based on this, we introduce the sharpness-aware minimization to mitigate CF by flattening the loss landscape. Experiments on three widely-used fine-tuning datasets, spanning different model scales, demonstrate the effectiveness of our method in alleviating CF. Analyses show that we nicely complement the existing anti-forgetting strategies, further enhancing the resistance of LLMs to CF.