We experimentally demonstrate the first use of 1550-nm InAs/GaAs quantum dot semiconductor saturable absorber mirror (QD-SESAM) in the dual-wavelength passively Q-switched (QS) erbium doped fiber (EDF) laser. The dual-wavelength QS lasing was obtained at a pump threshold of 180 mW with the average output power of 2.2 mW and the spacing between the two lasing wavelengths is 14 nm. A large absorption ranging from 1520 to 1590 nm has been realized when no substrate rotation was employed during the molecular beam epitaxy growth of the QD-SESAM indicating the potential to generate a 60 nm spacing of the dual-wavelength QS lasing peaks by changing the positions in the QD-SESAM and replacing EDF by co-doped fiber as gain medium. These results have provided a new opportunity towards achieving the stable and wide wavelength-tunable dual-modes fiber lasers.