This paper presents PipeBoost, a low-latency LLM serving system for multi-GPU (serverless) clusters, which can rapidly launch inference services in response to bursty requests without preemptively over-provisioning GPUs. Many LLM inference tasks rely on the same base model (e.g., LoRA). To leverage this, PipeBoost introduces fault-tolerant pipeline parallelism across both model loading and inference stages. This approach maximizes aggregate PCIe bandwidth and parallel computation across GPUs, enabling faster generation of the first token. PipeBoost also introduces recovery techniques that enable uninterrupted inference services by utilizing the shared advantages of multiple GPUs. Experimental results show that, compared to state-of-the-art low-latency LLM serving systems, PipeBoost reduces inference latency by 31% to 49.8%. For certain models (e.g., OPT-1.3B), PipeBoost achieves cold-start latencies in the range of a few hundred microseconds.