Positron annihilation lifetime spectra have been measured in carbon nanotubes being pressed as a function of pressure up to 1536MPa. In addition, positron lifetime experiments for carbon nanotubes in vacuum, nitrogen and air have been performed respectively. Lifetimes have been obtained using LIFETIME program. The results display a single-component positron annihilation lifetime. Positron lifetime for carbon nanotubes decreases as the pressure increases, but lifetime is basically consistent after the pressure of 960MPa. Positron annihilation lifetime for carbon nanotubes in air is the shortest whereas the lifetime in vacuum the longest. We conclude that a positron annihilates with an electron on the external surface of carbon nanotubes.