Airport networks are interconnected through flight routes, with delays at upstream airports leading to delays at downstream airports, thus causing delay propagation. Exploring the mechanisms of delay propagation in airport networks provides scientific insights for managing and controlling delays in aviation systems. Existing methods, such as Granger causality tests and transfer entropy, must be revised to address the nonlinear causal relationships of delays in airport networks. So, this paper proposes a causality mining method for delay propagation in airport networks based on partial correlation-based multivariate conditional independence (PCMCI). This method comprehensively considers all airports and causality mining in two stages. The first stage uses conditional independence tests to obtain the parent node set of the target airport, which includes both true and false causal relationships. The second stage employs instantaneous conditional independence tests to eliminate false causal relationships and obtain test statistics representing the strength of causality. Based on historical delay data from US airports over a year, the experimental results show that multiple factors cause delay propagation in airport networks rather than a single causal relationship. The scope of delay propagation is limited, mainly affecting a few airports closely connected to it. Delays at airports with small flight volumes are more likely to propagate. Few airport pairs in the network mutually propagate delays and, often, delays at airports affected by a particular airport’s delay also exhibit causal relationships with each other. This method provides a new perspective for deepening the understanding of delay propagation mechanisms in airport networks.