Winter wheat is a widely-grown cereal crop worldwide. Using growth-stage information to estimate winter wheat yields in a timely manner is essential for accurate crop management and rapid decision-making in sustainable agriculture, and to increase productivity while reducing environmental impact. UAV remote sensing is widely used in precision agriculture due to its flexibility and increased spatial and spectral resolution. Hyperspectral data are used to model crop traits because of their ability to provide continuous rich spectral information and higher spectral fidelity. In this study, hyperspectral image data of the winter wheat crop canopy at the flowering and grain-filling stages was acquired by a low-altitude unmanned aerial vehicle (UAV), and machine learning was used to predict winter wheat yields. Specifically, a large number of spectral indices were extracted from the spectral data, and three feature selection methods, recursive feature elimination (RFE), Boruta feature selection, and the Pearson correlation coefficient (PCC), were used to filter high spectral indices in order to reduce the dimensionality of the data. Four major basic learner models, (1) support vector machine (SVM), (2) Gaussian process (GP), (3) linear ridge regression (LRR), and (4) random forest (RF), were also constructed, and an ensemble machine learning model was developed by combining the four base learner models. The results showed that the SVM yield prediction model, constructed on the basis of the preferred features, performed the best among the base learner models, with an R2 between 0.62 and 0.73. The accuracy of the proposed ensemble learner model was higher than that of each base learner model; moreover, the R2 (0.78) for the yield prediction model based on Boruta’s preferred characteristics was the highest at the grain-filling stage.