A passively 2 μm Q-switched mode-locked thulium-doped fiber laser by using graphene saturable absorber on tapered fiber is experimently demonstrated. The pulse evolution with the increase of the pump power is discussed in the experiment. Finally stable Q-switched mode-locked pulse is obtained. Stable Q-switched pulse trains occurr at 390 mW pump power and the repetition rate is 19.5 kHz.When the pump power increases to 490 mW, Q-switched mode-locked pulse can be obtained. The Q-switched frequency is recorded with a frequency of 30.2 kHz and the mode-locked frequency is 19.5 MHz. After increasing the pump power to 610 mW, the mode-locked pulses are filled up with the Q-switched envelope. The Q-switched frequency is 44.9 kHz and mode-locked frequency is still 19.5 MHz.