Timely and accurate monitoring of winter wheat yields is beneficial for the macro-guidance of agricultural production and for making precise management decisions throughout the winter wheat reproductive period. The accuracy of crop yield prediction can be improved by combining unmanned aerial vehicle (UAV)-based multispectral data with deep learning algorithms. In this study, 16 yield-sensitive vegetation indices were constructed, and their correlations were analyzed based on UAV multispectral data of winter wheat at the heading, flowering, and filling stages. Seven input variable sets were obtained based on the combination of data from these three periods, and four generalized machine learning algorithms (Random Forest (RF), K-Nearest Neighbor (KNN), Bagging, and Gradient Boosting Regression (GBR)) and one deep learning algorithm (1D Convolutional Neural Network (1D-CNN)) were used to predict winter wheat yield. The results showed that the RF model had the best prediction performance among the generalised machine learning models. The CNN model achieved the best prediction accuracy based on all seven sets of input variables. Generalised machine learning models tended to underestimate or overestimate yields under different irrigation treatments, with good prediction performance for observed yields < 7.745 t·ha−1. The CNN model showed the best prediction performance based on most input variable groups across the range of observed yields. Most of the differences between observed and predicted values (Yi) for the CNN models were distributed between −0.1 t·ha−1 and 0.1 t·ha−1, and the model was relatively stable. Therefore, the CNN model is recommended in this study for yield prediction and as a reference for future precision agriculture research.