Recent advancements in Large Language Models (LLMs) have emphasized the critical role of fine-tuning (FT) techniques in adapting LLMs to specific tasks, especially when retraining from scratch is computationally infeasible. Fine-tuning enables LLMs to leverage task- or domain-specific data, producing models that more effectively meet the requirements of targeted applications. However, conventional FT approaches often suffer from catastrophic forgetting and suboptimal data efficiency, limiting their real-world applicability. To address these challenges, this paper proposes \textbf{DEAL}, a novel framework that integrates Low-Rank Adaptation (LoRA) with a continuous fine-tuning strategy. By incorporating knowledge retention and adaptive parameter update modules, the framework mitigates the limitations of existing FT methods while maintaining efficiency. Experiments on 15 diverse datasets show that DEAL consistently outperforms baseline methods, yielding substantial gains in task accuracy and resource efficiency. These findings demonstrate the potential of our approach to advance continual adaptation in LLMs by enhancing task performance while improving resource efficiency. The source code is publicly available at https://github.com/zzm-black/DEAL-Continuous-Low-Rank-Fine-Tuning.