The carbon nanotube as a saturable absorber is used in the passively Q-switched and Q-switched mode-locking (QML) of a laser diode (LD) pumped Tm:YAP operating at 2 μm. As high as 507 mW average output power of Q-switched pulses laser is obtained with a pump power of 8.64 W at the cavity length of 30 mm. The maximum pulse energy, pulse width and pulse repetition frequency are 18.8 μJ, 262 ns and 26.91 kHz respectively. When the whole cavity length increases to 80 mm, the QML laser is obtained. The maximum average output power and the pulse repetition frequency of Q-switched envelope are 387 mW and 34.61 kHz, respectively, while the pulse repetition frequency of the mode locking is 1.87 GHz.