Detecting training data for large language models (LLMs) is receiving growing attention, especially in applications requiring high reliability. While numerous efforts have been made to address this issue, they typically focus on accuracy without ensuring controllable results.To fill this gap, we propose Knockoff Inference-based Training data Detector (KTD), a novel method that achieves rigorous false discovery rate (FDR) control in training data detection. Specifically, KTD generates synthetic knockoff samples that seamlessly replace original data points without compromising contextual integrity. A novel knockoff statistic, which incorporates multiple knockoff draws, is then calculated to ensure FDR control while maintaining high power. Our theoretical analysis demonstrates KTD's asymptotic optimality in terms of FDR control and power. Empirical experiments on real-world datasets such as WikiMIA, XSum and Real Time BBC News further validate KTD's superior performance compared to existing methods.