Accurate estimation of the leaf area index (LAI) is essential for crop growth simulations and agricultural management. This study conducted a field experiment with rice and measured the LAI in different rice growth periods. The multispectral bands (B) including red edge (RE, 730 nm ± 16 nm), near-infrared (NIR, 840 nm ± 26 nm), green (560 nm ± 16 nm), red (650 nm ± 16 nm), blue (450 nm ± 16 nm), and visible light (RGB) were also obtained by an unmanned aerial vehicle (UAV) with multispectral sensors (DJI-P4M, SZ DJI Technology Co., Ltd.). Based on the bands, five vegetation indexes (VI) including Green Normalized Difference Vegetation Index (GNDVI), Leaf Chlorophyll Index (LCI), Normalized Difference Red Edge Index (NDRE), Normalized Difference Vegetation Index (NDVI), and Optimization Soil-Adjusted Vegetation Index (OSAVI) were calculated. The semi-empirical model (SEM), the random forest model (RF), and the Extreme Gradient Boosting model (XGBoost) were used to estimate rice LAI based on multispectral bands, VIs, and their combinations, respectively. The results indicated that the GNDVI had the highest accuracy in the SEM (R2 = 0.78, RMSE = 0.77). For the single band, NIR had the highest accuracy in both RF (R2 = 0.73, RMSE = 0.98) and XGBoost (R2 = 0.77, RMSE = 0.88). Band combination of NIR + red improved the estimation accuracy in both RF (R2 = 0.87, RMSE = 0.65) and XGBoost (R2 = 0.88, RMSE = 0.63). NDRE and LCI were the first two single VIs for LAI estimation using both RF and XGBoost. However, putting more than one VI together could only increase the LAI estimation accuracy slightly. Meanwhile, the bands + VIs combinations could improve the accuracy in both RF and XGBoost. Our study recommended estimating rice LAI by a combination of red + NIR + OSAVI + NDVI + GNDVI + LCI + NDRE (2B + 5V) with XGBoost to obtain high accuracy and overcome the potential over-fitting issue (R2 = 0.91, RMSE = 0.54).