The high-precision time-frequency transfer of the optical atomic clock signals over ground-to-satellite and terrestrial free-space laser paths is of great significance in the fields of fundamental and applied sciences. However, the phase noises caused by atmospheric turbulence severely degrade the measurement precision. In this paper, a new method to simulate the transmission of time-frequency signal propagating through atmospheric turbulence is investigated. An analog transmission system comparable to the practical out-field link has been demonstrated, which can provide a deep insight into the phase distortion of time-frequency signal of free-space optical communication links.