We report a new single-walled carbon nanotube (SWNT)-induced re-entrant lyotropic phase behavior of Pluronic F127 block copolymers in water which show two hexagonal phase regions. The small angle X-ray scattering measurements show that as the concentration is increased from 5 to 100 wt% by evaporation, the F127-SWNT/water system exhibits isotropic-hexagonal-(FCC/hex)-BCC-hexagonal-lamellar phase transitions, which is in contrast to the F127/water system showing isotropic-FCC-BCC-hexagonal-lamellar phase transitions. This clearly indicates that, in the F127-SWNT/water system, the 1st hexagonal phase is induced by the presence of long one-dimensional SWNTs and the 2nd hexagonal phase originates from the phase behavior of F127 itself. The presence of SWNTs also induced the shifts of phase transition concentrations and the change of domain sizes. The SWNTs in the hexagonal phases are located in the hydrophobic core (PPO domain) of F127 cylinders, making their orientation parallel to the  direction. The possible orientations of SWNTs (which maintain their individuality or very small bundle state) in the FCC and BCC phases were identified based on the epitaxial transitions between corresponding phases (hexagonal to FCC, FCC to BCC, and BCC to hexagonal):  in the FCC and < 111 > in the BCC.