Based on the rate equation, a mathematic model of laser diode (LD) pumped gain-switched Nd:YVO4 microchip laser under pre-pumping together with pulse pumping mechanism is presented. This model well shows the temporal characteristics of output pulses when the pumping parameters vary slightly. The results of numerical simulation indicate that the width of the output pulses changes little when the increase of pumping parameters is below 10%, however, the number of the output pulses increases rapidly and has a nonlinear monotone increasing relation with the pumping parameters. The experimental results of such gain-switched microchip laser are measured under the corresponding pumping conditions. It is found that the numerical and experimental results match with each other very well.