An L-band switchable dual-wavelength passively mode-locked fiber laser based on a carbon-nanotube saturable absorber is reported herein. The central wavelength of the fiber laser spectrum can switch between 1572.9 nm and 1596.6 nm with a pulse width of 1.80 ps by tuning the pump power; the corresponding 3-dB spectral widths of the two wavelengths are 3.68 nm and 2.34 nm, respectively. Additionally, the dual-wavelength mode-locked fiber laser has a wavelength separation of ~24.8 nm, with two central wavelengths of 1572.3 nm and 1597.1 nm, respectively. A numerical study is conducted on the formation and evolution of the L-band switchable dual-wavelength mode-locked fiber laser. The numerical results are in good agreement with the experimental observations, indicating that the switchable dual-wavelength mode-lock can be attributed to the change in the transmission spectrum of the gain fiber.