A compact diode-end-pumped passively Q-switched laser was built up with a Yb:YAG/Cr4+:YAG/YAG composite crystal for generating a high-peak-power and short-pulse laser at 1 029 nm. The affect and mechanism of pump power and initial transmission on output pulsed performances were studied. By experimental comparison, it is found that the composite crystal with initial transmission of 85% gets the best pulsed performances, which the pulse peak power reaches to 87 kW with pulse width of 3.14 ns at incident pump power of 7.2 W. Moreover, variation of output spectrum with incident pump power is studied, which reveals that this composite crystal has good thermal property. Therefore, both bonding nondoped YAG crystal and using low initial transmission can contribute to high-peak-power and short-pulse laser output.