A theoretical investigation of the influence of pump parameters of quasi-continuous-wave laser-diode (LD) pumped Yb∶KYW/Cr⁴⁺∶YAG laser on pulse characteristics based on passively Q-switched rate equations is presented. Through numerical calculation, the relationship between the characteristics of Q-switched pulse delay, pulse width, sub-pulse sequence, and pump rate is analyzed to obtain the optimal pump-light duty cycle and effectively reduce the thermal effect caused by continuous-wave pump. Furthermore, the high-repetition-rate LD pump source is used in the experiment, and the accurate locking and control of output characteristics such as repetition rate, pulse delay, and the number of pulse trains of the passively Q-switched laser are realized by adjusting the pump parameters. When the duty cycles of 15.6-W pump power are 6.5%, 8%, and 9.65%, stable outputs of single pulse, double pulse, and triple pulse, respectively, are obtained, and the coupling resonance of pump pulse and laser pulse is improved. The experimental results are in agreement with the theoretical calculation.