Federated low-rank adaptation (LoRA) enables multiple clients to collaboratively fine-tune large language models (LLMs) without disclosing their raw data. However, existing works often experience performance degradation due to biased model aggregation and are hindered by significant communication and computation burden, both limiting training efficiency. In this paper, we propose iFLoRA, an improved Federated LoRA fine-tuning system for LLMs featuring pipelined error-mitigated model aggregation and adaptive matrix-wise parameter freezing. Specifically, iFLoRA mitigates aggregation error by first reconstructing local update matrices from clients’ low-rank matrices. These are then aggregated into a global update, which is decomposed via singular value decomposition (SVD) to form low-rank matrices for the next round. To mitigate the overhead from SVD, iFLoRA employs a pipeline to overlap global aggregation, local computation, and communication. Additionally, iFLoRA implements an adaptive matrix-wise freezing scheme that assesses their stability and selectively freezes them for adaptively adjusted periods, alleviating client training overheads without compromising model performance. Extensive experiments on real-world datasets show that iFLoRA can improve time-to-target by 2.17-8.48× than state-of-the-art methods. Our code is available at: https://github.com/whr819987540/iflora.