We have investigated the longitudinal magnetoresistance (MR) of thin films of single-walled carbon nanotubes, in pulsed magnetic field up to 32T. We report the longitudinal MR markedly different from the transverse MR. At T=38.5K, the longitudinal MR exhibits a pronounced positive MR and saturates around 20T, while the transverse MR remained negative for similar carbon nanotube films. With decreasing temperature down to 11K, the negative contribution to the MR increases at low field and the positive contribution diminishes. The minimum of the MR, thus, appears at a higher field with lowering T, for the temperature range between 11 and 38.5K. On the other hand, below 10K, the longitudinal MR behaves similar to the transverse MR. The behaviors of the longitudinal MR are distinguished across T∼11K, and they might have different origin. We suggest Aharonov–Bohm effect, which tunes the band structure of the CNTs by the field parallel to the tube axis, may play a role.