Hyperspectral remote sensing using Unmanned Aerial Vehicles (UAVs) provides accurate, near-real-time, and large-scale spatial estimation of leaf area index (LAI), a very important crop variable used for monitoring crop growth. In the present study, the LAI of wheat crops was estimated using high-resolution UAV-borne hyperspectral data with a spectral range of 400-1000nm and a spatial resolution of 4cm. A total of twenty-seven hyperspectral vegetation indices were computed. The PLS (Partial Least Squares) regression combined with the VIP (Variable Importance in the Projection) scores were used for selecting the optimum indices as feature vectors for the Extreme Gradient Boosting (Xgboost) model for predicting LAI. The twelve optimal vegetation indices with VIP scores above 1 were selected to develop the prediction model. Once validated against the in situ-measured LAI values, the prediction model showed good accuracy, with R2 of 0.71, RMSE of 0.52, and MAE of 0.44. The model was used to generate a spatial map showing the variability in the LAI of wheat fields. Accurate mapping of LAI for wheat crops was achieved by integrating high-resolution UAV data and machine learning models. The results can be up-scaled to farmers’ fields for the operational delivery of LAI of crops to monitor crop growth and predict yield.