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A diode-end-pumped Q -switched mode-locking Nd:GdVO4 laser operating at 1.34 μm with an acousto-optical (AO) Q-switch in a compact V-type cavity was realized in our experiment for the first time. When the AO Q-switch repetition rate was 10 kHz, the maximum average output power of 750 mW and the pulse energy of 75 μ were obtained at the maximum incident pump power of 9 W. The mode-locking modulation depth of about 100% was obtained at certain pump power over the threshold. The mode-locked pulse inside in the Q-switched pulse had a repetition rate of 341 MHz, and its average pulsewidth was estimated to be about 350 ps. A developed rate equation model for the Q -switched and mode-locked lasers with an AO Q-switch were proposed by using the hyperbolic secant functional methods. The results of numerical calculations of the rate equations were in good agreement with the experimental results.