In order to evaluate the impact of atmospheric refractive index distribution on timing deviation of time transfer by space laser link at double wavelengths, we propose the model of atmospheric refractive index distribution influenced on timing deviation with the measured meteorological data. The asymmetric delay deviation and the position deviation of the transceiver terminal are simulated respectively in different regions, different months and different zenith angles based on the ground terminal capturing mode and the satellite terminal capturing mode. The results show that the asymmetric delay deviation and the position deviation are smaller when the atmospheric pressure is lower and the atmospheric temperature is higher. The timing deviation of satellite terminal capturing mode is hundreds of picoseconds. The timing deviation of the ground terminal capturing mode reaches to nanoseconds, which can be decreased to about ten picoseconds by further bidirectional precision alignment. In the satellite passing time, the asymmetric delay deviation and position deviation change with the variation of the zenith angle, and there are geographical location differences between the ground terminals. In general, it is necessary to correct the asymmetric delay deviation and the position deviation of transceiver terminals in real time.