With the widespread application of unmanned aerial vehicles (UAVs), the safety detection system of UAVs has created an urgent need for anomaly detection technology. As a direct representation of system health status, flight data contain critical status information, driving data-driven methods to gradually replace traditional dynamic modeling as the mainstream paradigm. The former effectively circumvent the problems of nonlinear coupling and parameter uncertainty in complex dynamic modeling. However, data-driven methods still face two major challenges: the scarcity of anomalous flight data and the difficulty in extracting strong spatio-temporal coupling among flight parameters. To address these challenges, we propose an unsupervised anomaly detection method based on the causality-enhanced graph neural network (CEG). CEG innovatively introduces a causality model among flight parameters, achieving targeted extraction of spatial features through a causality-enhanced graph attention mechanism. Furthermore, CEG incorporates a trend-decomposed temporal feature extraction module to capture temporal dependencies in high-dimensional flight data. A low-rank regularization training paradigm is designed for CEG, and a residual adaptive bidirectional smoothing strategy is employed to eliminate the influence of noise. Experimental results on the ALFA dataset demonstrate that CEG outperforms state-of-the-art methods in terms of Precision, Recall, and F1 score. The proposed method enables accurate and robust anomaly detection on a wide range of anomaly types such as engines, rudders, and ailerons, validating its effectiveness in handling the unique challenges of UAV anomaly detection.