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Recently, Knowledge Graphs (KGs) have been successfully coupled with Large Language Models (LLMs) to mitigate their hallucinations and enhance their reasoning capability, e.g., KG-based retrieval-augmented framework. However, current KG-LLM frameworks lack rigorous uncertainty estimation, limiting their reliable deployment in applications where the cost of errors is significant. Directly incorporating uncertainty quantification into KG-LLM frameworks presents a challenge due to their more complex architectures and the intricate interactions between the knowledge graph and language model components. To address this crucial gap, we propose a new trustworthy KG-LLM framework, UAG (Uncertainty Aware Knowledge-Graph Reasoning), which incorporates uncertainty quantification into the KG-LLM framework. We design an uncertainty-aware multi-step reasoning framework that leverages conformal prediction to provide a theoretical guarantee on the prediction set. To manage the error rate of the multi-step process, we additionally introduce an error rate control module to adjust the error rate within the individual components. Extensive experiments show that UAG can achieve any pre-defined coverage rate while reducing the prediction set/interval size by 40% on average over the baselines.