Automatic Dependent Surveillance-Broadcast (ADS-B) systems face security challenges due to their unencrypted, open architecture, making them vulnerable to sophisticated attacks threatening aviation safety. Existing research primarily addresses single-dimensional anomaly detection, leaving gaps in identifying multidimensional compound anomalies characterizing real-world attacks. This paper proposes a hybrid Kolmogorov-Arnold Networks and Long Short-Term Memory (KAN-LSTM) model for robust ADS-B anomaly detection. Key contributions include: applying Kolmogorov-Arnold theorem to model complex nonlinear spatiotemporal relationships through adaptive activation functions; implementing entropy-based dynamic threshold strategy enabling adaptive sensitivity across flight phases; and comprehensive evaluation on real-world ADS-B data across seven anomaly scenarios. Experimental results demonstrate F1 scores of 93.75%–98.33%, outperforming state-of-the-art methods by 1.91% average and 4.1% for complex spoofing attacks. The approach enhances aviation security without requiring protocol modifications or equipment overhauls.