By considering the Guassian transversal distribution of intracavity photon density and the longitudinal distribution of photon density along the cavity axis as well as the influence of the turn-off time of the acousto-optic Q switch, we introduce the coupled rate equations of a laser-diode, end-pumped, double Q-switched laser with an acousto-optic modulator and GaAs saturable absorber. In addition the thermal effect of the gain medium is taken into account. These coupled rate equations are solved numerically, and the dependence of pulse width on incident pump power at different pulse repetition rates is obtained for the generated output pulses. It is shown that the pulse duration is obviously shorter in contrast to the actively Q-switched Nd:YVO4 laser with an acoustic-optic modulator, and the maximum compression ratio of the pulse width is more than 60%. In the experiment a laser-diode, end-pumped, double Q-switched Nd:YVO4 laser with both an acousto-optic modulator and GaAs is realized, and the experimental results agree with the numerical solutions.