Chlorophyll is an important component of crop photosynthesis as it is necessary for the material exchange between crops and the atmosphere. The amount of chlorophyll present reflects the growth and health status of crops. Spectral technology is a feasible method for obtaining crop chlorophyll content. The first-order differential spectral index contains sufficient spectral information related to the chlorophyll content and has a high chlorophyll prediction ability. Therefore, in this study, the hyperspectral index data and chlorophyll content of soybean canopy leaves at different growth stages were obtained. The first-order differential transformation of soybean canopy hyperspectral reflectance data was performed, and five indices, highly correlated with soybean chlorophyll content at each growth stage, were selected as the optimal spectral index input. Four groups of model input variables were divided according to the following four growth stages: four-node (V4), full-bloom (R2), full-fruit (R4), and seed-filling stage (R6). Three machine learning methods, support vector machine (SVM), random forest (RF), and back propagation neural network (BPNN) were used to establish an inversion model of chlorophyll content at different soybean growth stages. The model was then verified. The results showed that the correlation coefficient between the optimal spectral index and chlorophyll content of soybean was above 0.5, the R2 period correlation coefficient was above 0.7, and the R4 period correlation coefficient was above 0.8. The optimal estimation model of soybean and chlorophyll content is established through the combination of the first-order differential spectral index and RF during the R4 period. The optimal estimation model validation set determination coefficient (R²) was 0.854, the root mean square error (RMSE) was 2.627, and the mean relative error (MRE) was 4.669, demonstrating high model accuracy. The results of this study can provide a theoretical basis for monitoring the growth and health of soybean crops at different growth stages.