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The leaf area index (LAI) is a key parameter for describing the canopy structure of apple trees. This index is also employed in evaluating the amount of pesticide sprayed per unit volume of apple trees. Hence, numerous manual and automatic methods have been explored for LAI estimation. In this work, the leaf area indices for different types of apple trees are obtained in terms of multispectral remote-sensing data collected with an unmanned aerial vehicle (UAV), along with simultaneous measurements of apple orchards. The proposed approach was tested on apple trees of the "Fuji", "Golden Delicious", and "Ruixue" types, which were planted in the Apple Experimental Station of the Northwest Agriculture and Forestry University in Baishui County, Shaanxi Province, China. Five vegetation indices of strong correlation with the apple leaf area index were selected and used to train models of support vector regression (SVR) and gradient-boosting decision trees (GBDT) for predicting the leaf area index of apple trees. The best model was selected based on the metrics of the coefficient of determination (R2) and the root-mean-square error (RMSE). The experimental results showed that the gradient-boosting decision tree model achieved the best performance with an R2 of 0.846, an RMSE of 0.356, and a spatial efficiency (SPAEF) of 0.57. This demonstrates the feasibility of our approach for fast and accurate remote-sensing-based estimation of the leaf area index of apple trees. [ABSTRACT FROM AUTHOR]