Inference for Large Language Models (LLMs) is computationally demanding. To reduce the cost of auto-regressive decoding, Key-Value (KV) caching is used to store intermediate activations, enabling GPUs to perform only the incremental computation required for each new token. This approach significantly lowers the computational overhead for token generation. However, the memory required for KV caching grows rapidly, often exceeding the capacity of GPU memory. A cost-effective alternative is to offload KV cache to CPU memory, which alleviates GPU memory pressure but shifts the bottleneck to the limited bandwidth of the PCIe connection between the CPU and GPU. Existing methods attempt to address these issues by overlapping GPU computation with I/O or employing CPU-GPU heterogeneous execution, but they are hindered by excessive data movement and dependence on CPU capabilities. In this paper, we introduce an efficient CPU-GPU I/O-aware LLM inference method that avoids transferring the entire KV cache from CPU to GPU by recomputing partial KV cache from activations while concurrently transferring the remaining KV cache via PCIe bus. This approach overlaps GPU recomputation with data transfer to minimize idle GPU time and maximize inference performance. Our method is fully automated by integrating a profiler module that utilizes input characteristics and system hardware information, a scheduler module to optimize the distribution of computation and communication workloads, and a runtime module to efficiently execute the derived execution plan. Experimental results show that our method achieves up to 35.8% lower latency and 46.2% higher throughput during decoding compared to state-of-the-art approaches.