In a free space optical communication (FSOC) system, atmospheric turbulence will increase the bit error ratio (BER) and impair FSOC link reliability. Since computational temporal ghost imaging (CTGI) has anti-interference, we present an FSOC system over atmospheric turbulence based on CTGI. The simulation results show that the BER performance of CTGI is better than on-off keying under different atmospheric turbulence regimes. To improve the performance of the CTGI scheme, the influence of the number of transmission samples and code length is analyzed. It is shown that BER performance improves with the increment of the number of samples, while code length has no impact. This scheme provides an idea for reliable communication over atmospheric turbulence and an important reference for improving wireless optical communication in an extreme environment.