We numerically examine the influences of the cladding index and the cladding thickness on the transmission bandwidth of the terahertz (THz) pipe waveguide. Numerical results show that, when the refractive index or the thickness of the cladding decreases, the transmission band becomes broader under either condition. However, the transmission band suffers a larger loss when the cladding index decreases. Hence, controlling the cladding thickness is the preferred mean to increase the transmission bandwidth.