Leaf Area Index (LAI) is an important parameter which can be used for crop growth monitoring and yield estimation. Many studies have been carried out to estimate LAI with remote sensing data obtained by sensors mounted on Unmanned Aerial Vehicles (UAVs) in major crops; however, most of the studies used only a single type of sensor, and the comparative study of different sensors and sensor combinations in the model construction of LAI was rarely reported, especially in soybean. In this study, three types of sensors, i.e., hyperspectral, multispectral, and LiDAR, were used to collect remote sensing data at three growth stages in soybean. Six typical machine learning algorithms, including Unary Linear Regression (ULR), Multiple Linear Regression (MLR), Random Forest (RF), eXtreme Gradient Boosting (XGBoost), Support Vector Machine (SVM) and Back Propagation (BP), were used to construct prediction models of LAI. The results indicated that the hyperspectral and LiDAR data did not significantly improve the prediction accuracy of LAI. Comparison of different sensors and sensor combinations showed that the fusion of the hyperspectral and multispectral data could significantly improve the predictive ability of the models, and among all the prediction models constructed by different algorithms, the prediction model built by XGBoost based on multimodal data showed the best performance. Comparison of the models for different growth stages showed that the XGBoost-LAI model for the flowering stage and the universal models of the XGBoost-LAI and RF-LAI for three growth stages showed the best performances. The results of this study might provide some ideas for the accurate estimation of LAI, and also provide novel insights toward high-throughput phenotyping of soybean with multi-modal remote sensing data.