A high power passively Q-switched laser of diode-pumped domestic Yb:YAG ceramic is reported in this paper. In the experiment, a semiconductor saturable absorber mirror (SESAM) is used as the Q-switching component, and the passively Q-switched laser pulse output is obtained under the absorbed pump power of 6.3 W. The maximum average output power of the Q-switched laser pulses is 1.24 W, the pulses′ duration is 2.93 μs, the repetition rate is 31 kHz, and the single pulse energy is 40 μJ. By studying the performance of the domestic Yb YAG ceramics under continuous and Q-switched laser, the potential applications of domestic high-quality Yb YAG ceramics in high-power short-pulse solid-state lasers are revealed.