Dielectric-coated metallic hollow fiber is one of the promising media for THz transmission. The dielectric layer enhances the reflection rate and hence lowers the transmission loss,whereas it brings additional loss due to its material absorption. The influence of dielectric absorption on the structure parameters of the hollow fiber is theoretically discussed. Calculation results show that the optimum refractive index of an absorptive dielectric layer is greater than that of a perfect transparent dielectric layer. The optimum thickness of the dielectric layer to minimize the loss of HE11 mode becomes smaller due to the absorption. The absorption tolerance is also investigated when considering such factors as inner diameter,refractive index,and transmission wavelength. It is shown that absorption tolerance decreases when the inner diameter becomes smaller or when the transmission wavelength becomes larger. In extreme cases of small inner-diameter or large transmission wavelength,the absorption tolerance is not existent. The calculation results are useful to the structure design and material selection in the fabrication of terahertz hollow fibers.