Single-walled carbon nanotubes (CNTs) are light and highly tensile, which makes them a candidate material for space elevator. However, CNTs are not resistant to oxidant. We studied the damage of CNTs caused by exposure to ozone using several kinds of single-walled CNTs with varying crystallinity and morphology. We found a correlation between the initial crystallinity and resistance to ozone : high-crystallinity CNTs with a small number of defects were lightly damaged by ozone exposure, while highly-defective CNTs were further damaged. The thickness of bundling also affected the resistance to ozone. High-crystallinity CNTs forming a thick bundle were most resistant to ozone.