Characteristics of Gradually-Tapered Hollow Waveguide(GTHW) are investigated for terahertz wave transmission. Based on the ray-optics method, simulation analysis is made in detail on beam profile and transmission attenuation. Compared with Constant Diameter Hollow Waveguide(CDHW), GTHW has unique properties when light travels from large end to small end or in the opposite direction. When light travels from large end to small end, GTHW and CDHW have similar additional losses caused by bending, and GTHW has much higher coupling efficiency and is convenient coupled with various light sources. When light travels from small end to large end, GTHW has lower transmission loss and an output beam with smaller divergence angle. Influences of waveguide parameters on transmission attenuation are simulated, such as bending radius, light source divergence angle, and the angle of the taper slope. Verification experiments are carried by using laser diode radiating at the wavelength of 532 nm. Measured data show good agreement with the simulation results.