A compact, all solid-state and high repetition rate as up to 105 kHz acousto-optic (A-O) Q-switched intracavity frequency-doubled 532 nm laser is demonstrated. A Nd∶YVO4 crystal is used as active media and a type-Ⅱ KTP (KTiPO4) as frequency doubler, The Q switcher is made by fused silica and driven by a driver whose maximal rf output power is 7.5 W and repetition rate is variable from 1 Hz to 105 kHz, which is made by our own. 224 mW of 532 nm average power at a repetition rate of 50 kHz was generated with a 1 W laser diode (LD) as pump source, and a high optical-to-optical conversion efficiency of 22.4% was obtained. Under low repetition rate, steady operation is achieved with pulse width of 17.2 ns, peak power of 470 W and single pulse energy of 8.1 μJ. A general formula of average-power as a function of pulse repetition rate is presented which has good agreement with the experiment results. Analysis and experimental verification showed that, even in four-level system, the effective storage time is not equal to the upper state lifetime.