Antioxidants are usually added to polymeric insulating materials to suppress oxidative degradation. However, the details of antioxidant added to a polymer are often not disclosed. On the other hand, compared to mid-infrared absorption spectroscopy, terahertz (THz) absorption spectroscopy, and far-infrared (FIR) absorption spectroscopy have not been performed so often. Based on the above backgrounds, six different kinds of antioxidants were added into low-density polyethylene sheets with four different contents, and their THz and FIR absorption spectra were measured. As a result, it has become clear that each antioxidant shows its specific absorption peaks, by which the antioxidants can be identified. Furthermore, the antioxidant content can be estimated by the absorption intensity of the specific peak. A chemometric analysis can make the estimation more accurately than a simple comparison of absorption intensity.