Laser sources with a controllable flexible wavelength have found widespread applications in optical fiber communication, optical sensing, and microscopy. Here, we report a tunable mode-locked fiber laser using a graphene-based saturable absorber and a tapered mirror as an end mirror in the cavity. The phase layer in the mirror is precisely etched by focused ion beam (FIB) milling technology, and the resonant wavelength of the mirror shifts correspond to the different etch depths. By scanning the tapered mirror mechanically, the center wavelength of a mode-locked fiber laser can be continuously tuned from 1562 to 1532 nm, with a pulse width in the sub-ps level and repetition rate of 27 MHz.