The liquid level of a steam generator is one of the key parameters for evaluating the operational status of a nuclear power plant. Traditional monitoring methods with preset fixed liquid level alarm thresholds fail to detect abnormalities early enough before triggering alarm signals. Therefore, it is necessary to establish an anomaly detection model for the steam generator liquid level. Considering the complex nonlinear characteristics of steam generator systems, NARX (nonlinear auto-regressive with exogenous inputs) method was used to study the coupling relationship model between the liquid level and related parameters under normal operating conditions. The model used historical liquid level values and related parameters as input regressors to predict the liquid level at the next time step. By comparing the predicted value with the actual observation, the magnitude of the residual could determine whether the current working state of the steam generator multi-sensor system was abnormal. Compared to traditional state monitoring methods that trigger alarms only after reaching preset liquid level thresholds, the results show that this method can detect deviations in the coupling relationship between the liquid level and related parameters and detect anomalies even with minor changes, thus enabling the monitoring and early warning of steam generator liquid levels. Validation with real nuclear power plant data demonstrates the model's ability to accurately regress liquid levels and achieve good anomaly detection performance in experiments using an abnormal dataset constructed based on real fault types.