Potassium content in soil is one of the important indicators for evaluating soil nutrient levels. There are few studies using thermal infrared emissivity data to invert potassium, and the model accuracy is low. In this paper, the Thermal Airborne Hyperspectral Imager (TASI) data collected in the Hailun region of Northeast China is used to investigate the relationship between soil emissivity and potassium content in black soil after pretreatment and separation of temperature and emissivity. Compared with the constant multiple stepwise regression and partial least-square regression model, a new stepwise regression method- quadratic multiple stepwise regression is innovatively used to enhance the model. Compared with the constant multiple stepwise regression, more parameters are introduced to establish the model, which can effectively improve the inversion accuracy. It is found that the model which uses effective special selected bands has a higher inversion accuracy to the potassium element and the selected bands are negatively correlated. The bands are 6 (8.602 μm), 11 (9.150 μm), 15 (9.588 μm), and 23 (10.464 μm)and the correlation coefficients are -0.658, -0.673, -0.645, -0.627, respectively. The quadratic multiple stepwise regression model’s RMSE of the training and testing data are 0.027 and 0.032, the decision coefficient R2 are 0.667 and 0.82. Compared to the constant multiple stepwise regression model’s RMSE of the training and testing data: 0.031 and 0.031, the decision coefficient R2: 0.569 and 0.78 and the least squares model’s RMSE: 0.033, 0.037, the judgment coefficient R2: 0.45, 0.51, the precisions of evalution indexes have been improved, it is indicated that this method effectively improved the inversion accuracy of the potassium element using the emissivity data. After using the studentized residuals to improve the model to remove the outliers, it is found that the training accuracy is significantly improved but the test accuracy is reduced. Over-fitting the training set data leads to the decline of the model generalization. Therefore, the model is not recommended to improve.