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Hyperspectral remote sensing crop growth monitoring technology, an essential instrument for developing contemporary precision agriculture, is characterized by non-destructiveness and real-time effectiveness. Taking leaf area index (LAI) of soybean at flowering stage under different levels of N application and mulching treatment as research object, the raw data for the hyperspectral reflectance of the soybean canopy were pretreated by using the 0~2 order differential transform processing (step 0.5). Based on five sets of pretreatment reflectance data, the optimum spectral index with a high correlation to the LAI of soybean at the blooming stage was the input data. And the support vector machine (SVM), random forest (RF), and BP neural network optimized by genetic algorithm (GA-BP) were used to construct the soybean LAI prediction model.The results showed that compared with the integer order and the raw hyperspectral reflectance, the spectral indices built from the fractional order differential preprocessed hyperspectral reflectance correlated better with the soybean LAI.The corresponding bands of different orders of optimal spectral indices concentrated in the red-edge band. The correlation between the spectral index and soybean LAI was increased and then decreased as the differential order was increased, and the accuracy of the prediction model showed the same pattern.When the input data were the same for all three machine learning techniques, the model created by RF had the highest accuracy. A thorough analysis determined that the soybean LAI prediction model built by using RF had the highest accuracy of prediction when the input variable was the 1.5-order differential optimal spectral index. The R2 of the model validation set was 0.880, the RMSE was 0.3200cm2/cm2, the NRMSE was 10.354% and the MRE was 9.572%. The research result can help advance the development of precision agricultural production by offering theoretical references for enhancing the inversion accuracy of soybean LAI hyperspectral prediction models.