Superposed-neutral-atom model and the finite-difference method (SNA-FD) is used to calculate the positron annihilation lifetime in single-walled carbon nanotube bundles with different diameters in a large range. We find that in single-walled carbon nanotube bundles，the main area where positron annihilation takes place，the main object that positron annihilates with, as well as the positron annihilation lifetime change regularly as the diameter of single-walled carbon nanotube bundles changes. The positron annihilation lifetime in single-walled carbon nanotube bundles with diameter between 0.8—1.6nm is calculated to be 332—470ps. It agrees well with the experimental result of 394ps.