A time-dependent performance function for the aqueduct structure was established based on concrete carbonation depth. The first three statistical moments were obtained using the point estimate method, and the calculation results of time-dependent reliability indices by three third-moment methods were comparatively analyzed. Furthermore, remaining service life prediction method for aqueducts based on the time-dependent reliability index was proposed. By taking the Shazibei Aqueduct in Hunan Province as an example, the failure probability and reliability index under the concrete carbonation failure mode were calculated, and the remaining service life prediction formula was obtained through data fitting. The results indicate that the third-moment method based on lognormal distribution exhibits the best accuracy and applicability, which is highly consistent with the Monte Carlo simulation results, with an error of 0.42%. The third-moment methods based on the square normal distribution and exponential function have higher calculation efficiency, but the errors are 8.23% and 9.31%, respectively. The proposed method can be used for life assessment and maintenance of aqueducts under carbonation failure conditions.