As the parameter size of language models becomes extremely large, fine-tuning them with limited resources has become a challenging task. Latest advancements in parameter-efficient fine-tuning (PEFT) techniques allow for adjustments to only a minor fraction of the parameters of these LLMs. Yet, most of PEFT methods may suffer from the following limitations: (1) As the rank decreases sharply, PEFT methods like LoRA and Adapter tuning will exhibit significant performance degradation in downstream tasks. (2) An accuracy gap between these methods and full fine-tuning (Full-FT) still exists. To tackle these problems, we propose a Low-Rank Direct Attention Adaptation (LoRaDA) method for efficient LLM fine-tuning. Specifically, we introduce a novel Low-rank Multi-head Attention Map Module (LMAM), which can bring negative attention to self-attention modules and learn low-rank attention weights directly, capturing the characteristics of downstream tasks. Furthermore, LMAM can serve as a plug-in to existing methods, such as LoRA and Adapter, providing state-of-the-art performance even with extreme low rank setting.Extensive experiments on various downstream tasks demonstrate the superior performance of our LoRaDA method. Specifically, LoRaDA even outperforms the full fine-tuning method by up to 2.1% on GLUE benchmark. As a plug-in, LMAM boosts the accuracy of LoRA by up to 27.7% with LLaMA-7B on Commonsense Reasoning benchmark.