To address the problem of limited wavelength output by a traditional fiber laser for its gain medium of rare-earth-ion-doped fiber owing to the size-dependent wavelength of quantum dots, an all-normal dispersion mode-locked fiber laser with PbSe quantum dot as the gain medium is demonstrated and studied through numerical simulation. A stable dissipative soliton of 1.7 μm is obtained by calculation. The buildup dynamics, evolution in the cavity, and output characteristics in a steady state of generating dissipative solitons using a PbSe quantum dot fiber laser are investigated systematically. Influences with respect to the length and doping concentration of the gain fiber and the length of the passive fiber are explored. The optimal gain fiber length and doping concentration obtained under a pump power of 0.1 W are 0.3 m and 12×10²¹ m^-3 respectively, corresponding to a pulse duration of 7.59 ps and a spectral width of 13.77 nm. However, the steady-state disappears beyond a passive fiber length range of 2-7 m. Furthermore, when the passive fiber is 0.1 m, a multi-wavelength output is generated by the laser, with 22 peaks, a spectral range of 1678-1724 nm, and an envelope width of 22.33 nm. In the time domain, a dual soliton is emitted with a width of 0.92 ps and a pulse interval of 4 ps. This work provides theoretical guidance for establishing and optimizing an ultrafast quantum dot fiber laser and a new option for fiber lasers of special wavelengths.