As an independent characteristic of electromagnetic radiation, the polarization of light is sensitive to the scattering and absorption characteristics of the mineral particles. The combination of polarization and infrared absorption spectroscopy is conducive to rapidly and accurately detecting the SiO2 content of metallurgical sandstone deposits. In this study, the 8–14 μm polarized infrared absorption spectra and the grade of the sandstone ore samples were used to analyse the spectral characteristics of the sandstone powder samples. Principal component analysis (PCA) and the successive projection algorithm (SPA) were used to reduce the dimension of the original data, first-order derivative, reciprocal logarithm, and multivariate scattering correction (MSC) data. Then, generalized regression neural network (GRNN), partial least squares regression (PLSR), and convolutional neural network (CNN) were employed to establish a hyperspectral prediction model of SiO2 grade. The results show that the quantitative model by the PCA-CNN algorithm has the better prediction precision for the reciprocal logarithm data, with a coefficient of determination (R2), root mean square error (RMSE), and ratio of performance to interquartile range (RPIQ) of 0.907, 0.023, and 5.11, respectively. This method indicates that the polarized infrared absorption spectra and the PCA-CNN model can provide a more robust and significant spectral interpretation than single infrared spectra, and it is expected to be applied to any high-purity quartz deposit type for in situ and rapid analysis.