Based on the rate equation of passively Q-switching, the effects of pump rate on the pulse timing jitter was simulated. The evolution of pulse jitter versus initial transmittance of the saturated absorber and pump power were experimentally investigated using different Nd:YAG/Cr:YAG bonded crystals. By adopting reasonable parameters, it was proved that the pulse jitter of passively Q-switching could be controlled within hundreds of nanoseconds. If an actively Q-switched laser was used as the seed laser for a passively Q-switched microchip laser, the pulse jitter could be reduced down to ~5 ns, and the output characteristics of the passively Q-switched laser with seed injection were discussed.