Novel multi-wavelength passively mode-locked erbium-doped fiber laser based on single-walled carbon nanotube/polyimide film and Mach-Zehnder filter is proposed. A 3.2-m length of erbium-doped fiber acts as a gain medium. It is forward pumped by a 980-nm laser diode. The single-walled carbon nanotubes acts as mode locking devices. When pump power adds to 24 mW, the laser produces a stable pulse train with central wavelength of 1559.3 nm, 3 dB spectral width of 1.4 nm and average power of 0.8 mW. Then the Mach-Zehnder filter is introduced in the ring cavity as a comb filter. When the pump power is 25 mW, a stable 15-wavelength laser pulse is obtained by adjusting the polarization controller at the room temperature. The wavelength interval is 0.1 nm. The fiber laser can obtain stable multi-wavelength pulse train after continuous observation over 0.5 h.