This paper proposes a mode-locked fiber laser based on graphene-coated microfiber. The total length of the fiber laser resonant cavity is 31.34 m. Under the condition of stable output of bright-dark soliton pairs from the fiber laser, dual-wavelength tuning is realized by adjusting the polarization controller (PC), and the wavelength tuning range is 11 nm. Furthermore, the effects of polarization states on bright-dark solitons are studied. It is demonstrated that the mode-locking state can be switched between conventional solitons and bright-dark solitons in the graphene mode-locked fiber laser. Bright-dark soliton pairs with different shapes and nanosecond pulse width can be obtained by adjusting the PC and pump power.Graphical Abstract