Abstract: Thermal power units are the foundation of China's power supply and continue to play a dominant role in power production. Accurate prediction of NO_x concentration that adheres to physical constraints is crucial for combustion optimization, ensuring optimal operating conditions, and achieving energy conservation and emission reduction in coal-fired boilers. Machine learning can leverage historical operating data to build NO_x generation concentration prediction model with high fitting accuracy and fast calculation speed for complex boiler combustion systems. However, black-box models rely heavily on training data, lack interpretability, and may even contradict prior physical knowledge. To address this, a physics-constrained monotonic adaptive least squares support vector machine (MALSSVM) method was proposed for predicting NO_x generation concentration in coal-fired boilers. The proposed method integrated the prior physical monotonic relationships between oxygen content, coal feed rate, overfire air damper opening, and NO_x generation concentration into the adaptive least squares support vector machine (ALSSVM), so as to ensure the model to follow physical constraints, enhance prediction accuracy under different boiler operating conditions, and possess the capability to automatically adjust the model when object characteristics changes. A case study was conducted on a 660 MW coal-fired boiler. The analysis results indicate that the mean absolute error (MAE) of the prediction model on the test set is 20.84 mg/m³, representing a performance improvement of approximately 50%. The model can maintain monotonic relationships among relevant parameters under unknown operating conditions, aligning with actual physical constraints. It is significantly superior to the traditional ALSSVM method in terms of interpretability and generalization capability, providing more reliable technical support for the accurate prediction of NO_x concentration in thermal power units.