As an important part of the soil, the soil organic matter (SOM) can reflect soil fertility and quality. Compared with the traditional SOM measurement method, UAV hyperspectral images can quickly and real-time obtain the SOM content at the field-scale, which is of great significance for precision fertilization and sustainable utilization in the black soil region of Northeast China. In order to explore the difference in estimating the accuracy of SOM under crop cover by linear and nonlinear models based on hyperspectral data, the soil samples at the jointing stage and silking stage and UAV hyperspectral images were collected from the experimental corn field in the black soil region of Northeast China as the study area. The correlation between soil spectral reflectance and SOM content under crop cover was analyzed, and the spectral indices were calculated according to their response band. With the fertilizer rates and spectral indices as independent variables, multiple stepwise linear regression models (SMLR), support vector machine (SVM), random forest (RF) and eXtreme gradient boosting (XGBoost) models were established by screening characteristic variables, and the accuracies of the models were verified and compared (select R2 and RMSE as evaluation indicators). The results showed that the response band of SOM content under crop cover was 450~640 nm. Long-term application of chemical fertilizers had a significant effect on SOM content, and introducing it into the model as a covariate significantly improved the estimation accuracy of SOM. The test accuracies of the four models were: XGBoost>RF>SMLR>SVM, and the estimation result of XGBoost at the jointing stage was the best (R2 and RMSE of modeling set were 0.516, 0.253, and those of the verification set were 0.590, 0.222, respectively). Therefore, UAV hyperspectral technology can rapidly estimate SOM content in maize fields at field-scale, and the XGBoost model is a preferable option for estimating SOM content under crop cover conditions.