There is a serious concern that long term use of increasing amount of fossil fuels will cause significant climate changes. This concern arises from the inevitable production of CO2, which traditionally has been disposed of by direct dilution in air. In response, a variety of schemes for collection and disposal of CO2 have been investigated recently. Given the very large volumes of CO2 produced and the fact that storage would have to be permanent, the geological sequestration of CO2 is considered to be a better choice. While on the other hand, the static and dynamic properties of CO2 in porous geological media, such as the deep saline aquifers, depleted hydrocarbon reservoirs, or deep coal beds, are not fully understood, especially at the extreme conditions of high temperature and high pressure. In this work we report the study of the temperature (300K~500K), pressure (1bar~600bar) and diameter effects on adsorption and diffusion of CO2 through carbon nanotubes (CNTs) by the grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The simulation results suggest that the mobility of CO2 is slow in small CNTs, which is good for the sequestration of CO2. And the larger CNT can enfold more CO2 in its interior. Furthermore, the temperature and pressure have pronounced effects on the diffusion properties of CO2 in the CNTs.