A high-power high-repetition-rate acousto-optically Q-switched 1342 nm laser with double Nd:YVO4 crystals pumped by fiber-coupled laser diodes and simulated results based on Q-switched rate equations considering gain distribution on spectrum are presented. With total 40 W pump power incidence, the highest pulse repetition rate of 100 kHz was obtained. At 50 kHz repetition rate, average output power higher than 11 W and rather stable pulses were achieved. With the Q-switched rate equations considering gain distribution on spectrum, not only the pulse width, peak power and build-up time can be calculated, but the output distribution on the spectrum and its width can also be given. The experimental results are compared with the simulated ones. The model can be applied to analyze and design the spectrum of the laser output, and more exact results can be obtained because the practical gain distribution on the spectrum was taken into consideration.