Laser diode (LD) pumped passively Q-switched microchip laser has important applications in the field of industry, military, and medical treatment. To improve the output performance and system integration of LD pumped pulse microchip lasers, the Runge-Kutta method was used to solve the passively Q-switched laser rate equation, and the output parameters of LD end-pumped bonded Nd∶YAG/Cr4+∶YAG microchip laser was numerically simulated. The results show that with a 1mm/1.5mm bonded Nd∶YAG/Cr4+∶YAG as the gain medium, when the initial transmittance of Cr4+∶YAG is 75%, the transmittance of output mirror is 30%, and the radii of the pump and fundamental mode are 100μm, a 0.7W average power with pulse-width of 174ps at 16.1kHz can be obtained under the 4.5W pumping. This study has theoretical significance for the optimization and application of the passively Q-switched microchip laser.