Pre-trained Language Models (PLMs) have shown excellent performance on various downstream tasks after fine-tuning. Nevertheless, the escalating concerns surrounding user privacy have posed significant challenges to centralized training reliant on extensive data collection. Federated learning, which only requires training on the clients and aggregates weights on the server without sharing data, has emerged as a solution. However, the substantial parameter size of PLMs places a significant burden on the computational resources of client devices, while also leading to costly communication expenses. Introducing Parameter-Efficient Fine-Tuning(PEFT) into federated learning can effectively address this problem. However, we observe that the non-IID data in federated learning leads to a gap in performance between the PEFT method and full parameter fine-tuning(FFT). To overcome this, we propose FeDeRA, an improvement over the Low-Rank Adaption(LoRA) method in federated learning. FeDeRA uses the same adapter module as LoRA. However, the difference lies in FeDeRA's initialization of the adapter module by performing Singular Value Decomposition (SVD) on the pre-trained matrix and selecting its principal components. We conducted extensive experiments, using RoBERTa and DeBERTaV3, on six datasets, comparing the methods including FFT and the other three different PEFT methods. FeDeRA outperforms all other PEFT methods and is comparable to or even surpasses the performance of FFT method. We also deployed federated learning on Jetson AGX Orin and compared the time required by different methods to achieve the target accuracy on specific tasks. Compared to FFT, FeDeRA reduces the training time by 95.9\%, 97.9\%, 96.9\% and 97.3\%, 96.5\%, 96.5\% respectively on three tasks using RoBERTa and DeBERTaV3. The overall experiments indicate that FeDeRA achieves good performance while also maintaining efficiency.