In this paper, the material loss of anti-resonant hollow-core fiber (AR-HCF) and its properties are studied. We revisit the formula of power attenuation coefficient for the index-guiding optical fiber described by Snyder and Love in the 1980s and derive the modal overlap factor that governs the material loss of hollow-core fibers (HCF). The modal overlap factor formula predicts the material loss of AR-HCF, which agrees with numerical simulations by the finite element method. The optimization of silica-based AR-HCF design for the lowest loss at 4 µm wavelength is numerically discussed where the silica absorption reaches over 800 dB/m. Our work would provide practical guidance to develop low-loss AR-HCF at highly absorptive wavelengths, e.g. in the vacuum UV and mid/far-infrared spectral regions.