Superposed-neutral-atom model and the finite-difference method (SNA-FD) are used to calculate the positron annihilation lifetime in graphite, diamond and C60 We find that in graphite with laminar structure，the main place where the positron exists and annihilation takes place is the space between graphite layers. Positron lifetime of graphite is calculated to be 208ps, which agrees with the published experimental result. In diamond, the main place where positron exists and annihilation takes places is the space between carbon atoms. Positron lifetime of diamond is calculated to be 1150ps, which agrees with the published experimental result. In C60 with a fcc structure, the main area where positron exits is the space near the spherical molecule shell of C60 and the space between molecules. The main area where positron annihilation takes place is the space between molecules. Positron lifetime of C60 is calculated to be 352ps, which falls in the range of positron lifetime of C60 published in literature.