This paper proposes an algorithm-system co-optimization framework, FreeKV, to address the deployment challenges of large-scale language models (LLMs) with increasingly large context windows. The long contexts of LLMs pose deployment challenges due to the increasing size of the KV cache. Existing KV cache compression, elimination, and search methods suffer from poor accuracy or efficiency. FreeKV optimizes the KV selection and recall process through predictive search and fine-tuned corrections. It minimizes data transfer and improves efficiency through a hybrid KV layout between CPU and GPU memory and a double-buffered streaming recall. Experimental results demonstrate that FreeKV achieves up to 13x speedup over the best-performing KV search method, while maintaining nearly lossless accuracy across a variety of scenarios and models.