Large Language Models (LLMs) have showcased remarkable impacts across a wide spectrum of natural language processing tasks. Fine-tuning these pretrained models on downstream datasets provides further significant performance gains; however, this process typically requires a large number of expensive, high-end GPUs. Although there have been efforts focused on parameter-efficient fine-tuning, they cannot fully unlock the powerful potential of full-parameter fine-tuning. In this paper, we propose QFT, a Quantized Full-parameter Tuning framework for LLMs that quantizes and stores all training states, including weights, gradients, and optimizer states, in INT8 format to reduce training memory, thereby enabling full-parameter fine-tuning on existing GPUs at an affordable cost. To ensure training performance, we make two key efforts: i) for quantized gradients and optimizer states, we theoretically prove that the Lion optimizer, with its property of consistent update magnitudes, is highly robust to quantization; ii) and for quantized weights, we employ the hybrid feature quantizer, which identifies and protects a small subset of sparse critical features while quantizing the remaining dense features, thus ensuring accurate weight updates without FP32 backups. Moreover, to support backpropagation in the integer context, we develop a stack-based gradient flow scheme with O(1) complexity, forming a unified integer training pipeline. As a result, QFT reduces the model state memory to 21% of the standard solution while achieving comparable performance, e.g., tuning a LLaMA-7B model requires only <30GB of memory, making it feasible on a single A6000 GPU.