Direct measurements of the diffusion length of excitons in air-suspended single-walled carbon nanotubes are reported. Photoluminescence microscopy is used to identify individual nanotubes and to determine their lengths and chiral indices. Exciton diffusion length is obtained by comparing the dependence of photoluminescence intensity on the nanotube length to numerical solutions of diffusion equations. We find that the diffusion length in these clean, as-grown nanotubes is significantly longer than those reported for micelle-encapsulated nanotubes.