The fiber-pigtailed LiNbO3 electro-optical modulator with Mach-Zehnder(M-Z) structure is used as the active Q switching element. The all fiber active Q-switched laser at 1550 nm is realized with 974 nm diode laser as pump source and Yb-doped fiber with 110 dB/m peak absorption coefficient as gain medium. The periodic modulation of cavity loss is carried out with electro-optic intensity modulator. Q-switching action is realized and the stable Q-switched pulse output is obtained. The change laws of pulse width and peak power are investigated by changing pump power and modulation frequency. The stable output pulse can be obtained when the modulation frequency is adjusted from 50 Hz to 88 kHz. The most narrow pulse width of 246 ns and peak power about 5 W are obtained when the modulation frequency is 1 kHz.