We report the optical properties and exciton dynamics of undoped and hole-doped single-walled carbon nanotubes (SWCNTs). In the one-dimensional structures of SWCNTs, an electron and a hole form an exciton with a huge exciton binding energy. Stable excitons govern the optical responses of SWCNTs even at room temperature. With hole doping of SWCNTs, new peaks due to positive trions (positively charged excitons) appear below the E11 exciton peaks in the absorption and photoluminescence spectra. Trions are also stable at room temperature. Using femtosecond pump-probe transient absorption spectroscopy, we revealed that the exciton decay dynamics depends on the number of holes in SWCNTs. The exciton lifetime of hole-doped SWCNTs is much shorter than that of undoped SWCNTs. Fast decay components with lifetimes of a few picoseconds are attributed to trion formation and exciton-hole scattering in holedoped SWCNTs.