According to historical information, more than 300 metal smelting enterprises have been in the southwest of Xiongan for 300 years; however, these polluting enterprises have been gradually closed with the increased intensity of environmental protection. In the paper, 264 soil samples were collected and analyzed in the range of 400 nm–2500 nm by the spectra vista corporation (SVC), and the spectral noise was smoothed by the Savitzky–Golay filter. In order to enhance the spectral differences and curve shapes, mathematical transformations, such as the standard normal variate (SNV), first-order differential (FD), second-order differential (SD), multiple scattering correction (MSC), and continuum removal (CR), were performed on the data, and the correlation between spectral transformation and contents of REEs was analyzed. Moreover, three machine learning models—partial least-squares (PLS), random forest (RF), back propagation neural network (BPNN)—were used to predict the contents of REEs. Experimental results prove that REEs are combined with spectral active substances, such as organic compounds, clay minerals, and iron oxide, and it is possible to determine the contents of REEs using the reflection spectrum. The R² between the predicted values and measured contents reached 0.986 by using BPNN after FD transformation. More importantly, the predicted values basically agree with the actual situation for CASI/SASI airborne hyperspectral images, and this is an effective technique to obtain the contents of REEs in soil at the study area.