Leaf area index (LAI) is essential for evaluating crop growth and development. Destructive manual measurement methods mainly achieve traditional crop LAI acquisition. Due to the advantages of being fast and non-destructive, spectroscopy technology provides a feasible method for obtaining crop LAI. In order to achieve efficient acquisition of winter oilseed rape LAI, this study collected hyperspectral data and LAI data at the full-bloom stage of winter oilseed rape. It calculated the spectral indexes related to the LAI of the original spectrum and the first-order differential spectrum, respectively. The index with the highest correlation with the LAI of winter oilseed rape at the flowering stage was selected as the optimal spectral index for input. Subsequently, three machine learning methods, Back Propagation Neural Network (BPNN), Support Vector Machine (SVM), and Random Forest (RF), were used to construct the LAI model of winter oilseed rape, and the model was tested. The results show that the correlation coefficient between the spectral index calculated by the first-order differential processing of the original spectral data and the LAI of winter rapeseed is significantly improved compared with the original data. Among them, the spectral index NDVI with the best correlation coefficient with LAI can be obtained under the first-order differential: the correlation coefficient is 0.734, and the wavelength combination is 716 nm and 724 nm. At the same time, we found that when the input variables are the same, the RF model has higher estimation accuracy than the other models. The best estimation accuracy is obtained when the input variable is the first-order differential spectral index. The R2 of the model validation set is 0.810, RMSE is 0.455 cm2/cm2, MRE is 10.465%, and the model accuracy is high. The results of this study can provide a theoretical basis for crop monitoring based on spectral technology and provide a theoretical basis for crop growth.