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Yield prediction is of great significance in agricultural production. Remote sensing technology based on unmanned aerial vehicles (UAVs) offers the capacity of non-intrusive crop yield prediction with low cost and high throughput. In this study, a winter wheat field experiment with three levels of irrigation (T1 = 240 mm, T2 = 190 mm, T3 = 145 mm) was conducted in Henan province. Multispectral vegetation indices (VIs) and canopy water stress indices (CWSI) were obtained using an UAV equipped with multispectral and thermal infrared cameras. A framework combining a long short-term memory neural network and random forest (LSTM-RF) was proposed for predicting wheat yield using VIs and CWSI from multi-growth stages as predictors. Validation results showed that the R² of 0.61 and the RMSE value of 878.98 kg/ha was achieved in predicting grain yield using LSTM. LSTM-RF model obtained better prediction results compared to the LSTM with n R² of 0.78 and RMSE of 684.1 kg/ha, which is equivalent to a 22% reduction in RMSE. The results showed that LSTM-RF considered both the time-series characteristics of the winter wheat growth process and the non-linear characteristics between remote sensing data and crop yield data, providing an alternative for accurate yield prediction in modern agricultural management.