Charge mobilities of six DNAs and RNAs have been computed using quantum chemistry calculation combined with the Marcus-Hush theory. Based on this simulation model, we obtained quite reasonable results when compared with the experiment, and the obtained charge mobility strongly depends on the molecular reorganization and electronic coupling. Besides, we find that hole mobilities are larger than electron mobilities no matter in DNAs or in RNAs, and the hole mobility of 2L8I can reach 1.09 × 10-1 cm2 V-1 s-1 which can be applied in the molecular wire. The findings also show that our theoretical model can be regarded as a promising candidate for screening DNA- and RNA-based molecular electronic devices.