A broadband spectroscopy of anti-resonant waveguides in the terahertz region was investigated. The broadband spectral transmission properties of a poly(methylmethacrylate) (PMMA) pipe waveguide, a PMMA self-supporting waveguide, and a SiO2 pipe waveguide were studied using terahertz time domain spectroscopy (THz-TDS). The existence of the anti-resonance phenomenon was demonstrated. Additionally, the PMMA self-supporting waveguide has been experimentally shown to realize transmission bandwidth of over 2 THz without dip frequencies. Also, based on the anti-resonance mechanism, the dielectric pipe waveguide was successfully used as a terahertz refractive index sensor for liquid sensing, which offers a possible method for materials detection.