We report Q-switched mode-locked (QML) pulses generation in an Yb-doped multimode fiber (MMF) laser by using a graphene-deposited multimode microfiber (GMM) for the first time, to the best of our knowledge. The single-wavelength QML operation with the central wavelength tunable from 1028.81 nm to 1039.20 nm and the dual-wavelength QML operation with the wavelength spacing tunable from 0.93 nm to 5.79 nm are achieved due to the multimode interference filtering effect induced by the few-mode fiber and MMF structure and the GMM in the cavity. Particularly, in the single-wavelength QML operation, the fifth harmonic is also realized owing to the high nonlinear effect of the GMM. The obtained results indicate that the QML pulses can be generated in the MMF laser, and such a flexible tunable laser has promising applications in optical sensing, measuring, and laser processing.