In this paper, a subset simulation-based approach is proposed to tackle the network reliability analysis problem in supply chain risk assessment. The reliability of the supply chain is essential for seamless operations in modern businesses. Network reliability analysis evaluates the continuity and reliability of business operations in the event of failures occurring in nodes and paths within the supply chain system. Traditional methods for network reliability analysis often rely on computationally expensive Monte Carlo simulation due to the complexities and high-dimensional input space of supply chain systems. To overcome this challenge, a subset simulation-based approach is proposed in this paper. Subset simulation is an efficient method which employs importance sampling and Bayesian inference to accurately estimate the probability of extreme events. To implement the approach, the supply chain system is modeled as a network and sample uncertainties associated with input parameters. Subsequently, subset simulation techniques are utilized to generate a set of samples and evaluate the reliability of the supply chain system and assess potential risks. To validate the effectiveness of the proposed method, experiments are conducted on a real-world supply chain system. The results demonstrate that the approach achieves superior computational efficiency compared to traditional Monte Carlo simulation methods, while accurately assessing risks within the supply chain system.