The transmission characteristics of terahertz (THz) wave in turbulent atmosphere are very important for the application of THz wave in space. The horizontal transmission characteristics of THz wave in Kolmogorov turbulence atmosphere are studied. The variation of scintillation index and saturated distance of THz plane wave with the frequency, transmission distance and turbulence intensity in turbulent atmosphere is analyzed. Taking the Guassian beam as an example, the variation of the scintillation index and beam width of THz wave beams with the transmission distance in turbulence atmosphere is studied. The results show that in the THz wave band, the higher the frequency of THz wave is, the greater the scintillation index is and the shorter the saturated distance is. In general, when THz wave is transmitting in atmosphere, the influence of turbulence on it is between that on optical wave and that on microwave. For the short-range applications such as communication and imaging, THz wave is mostly in the state of weak fluctuation. But for the long-range applications such as THz radar and imaging, THz wave is in the state of strong fluctuation.