Parameters governing forward and reverse pumping of a device mechanism have an important influence on the cutoff and output characteristics of a drift-step-recovery diode (DSRD). Therefore, we analyzed the driving circuit for the DSRD that was used to adjust pumping parameter values. With multiple modules in parallel, a driving method exploiting narrow-pulse pumping is proposed in developing a high-repetition-frequency DSRD pulse generator. In experiments and simulations, one key factor affecting the working stability of this pulse generator operating at repetition frequencies in the megahertz range was found that helped in further optimizing the parameter settings of our 2 kV DSRD driving circuit. From this insight, a 2 kV-5 MHz all-solid-state high-repetition-frequency pulse generator based on the DSRD was developed.