A passively mode-locked alexandrite laser was developed with a single-walled carbon nanotubes (SWCNTs) saturable absorber (SA), which was pumped by a 638 nm red laser. After using a pair of prisms for dispersion compensation, the narrowest pulse width of 70 fs was achieved at a repetition rate of 100 MHz. The mode-locked laser had a signal-to-noise ratio greater than 55 dB and a beam quality factor of less than 1.13. A high average output power of 386 mW was achieved with a slope efficiency of 12.4%. It is the first time a passively mode-locked alexandrite femtosecond laser pumped by a 638 nm red laser has been developed. Moreover, it is also the first time that SWCNTs are used as SAs to achieve a passively mode-locked laser in the visible light range.