The propagation characteristics of terahertz (THz) wave in the turbulent atmosphere are very important to the space applications of THz wave. The horizontal propagation characteristics of THz wave in atmospheric turbulence have been studied by the random phase screen method. Through ignoring the scattering and absorption of THz atmospheric conditions and focusing on the atmospheric refractive index fluctuation, the average intensity distribution and scintillation indexes on the receiver plane were studied under different propagation distances in the atmospheric turbulence. For comparison, the visible light waves were also carried out through numerical simulation and analysis under the same conditions. The results show that under the same conditions, the influence of atmospheric turbulence on THz wave is much smaller than it on the visible light wave. Furthermore, atmospheric turbulence has little impact on the short-range application of THz wave.