Designing low-loss waveguides for terahertz waves is challenging as most materials are very lossy in this frequency band. Most scientists simply consider transmitting the waves through low-loss air, which however also has its own difficulties as index-guiding is not possible. In this paper, we report on the design of low-loss waveguides for terahertz waves and associated results by using a finite element leaky mode solver. These results show that waveguides designed using ARROW (anti-resonant reflecting optical waveguide) approach yield a low combined absorption and leakage loss down to only 0.05[Formula: see text]dB/cm for the q-TE[Formula: see text] fundamental mode using realistic values of refractive index at 1 THz operating frequency. The structure employs rectangular hollow-core and low-density polyethylene/air anti-resonant reflecting bilayers, which can be easily fabricated. These results are compared with those of other structures, i.e., a photonic crystal fiber-like structures using the same materials with rectangular holes, which is shown to give a higher loss of 3[Formula: see text]dB/cm and a suspended air-core waveguide with TOPAS vein offering a loss of 1[Formula: see text]dB/cm.