Using 940 nm diode laser as pumping source, a passively Q-switched Yb:YAG thin disk laser by Cr4+:YAG was realized. The Yb:YAG disk with 500 μm thickness was employed，the Yb3+ atom fraction is 10%.The distribution of temperature in Yb:YAG disk with direct water cooling and SiC cooling with different thickness was theoretically simulated, respectively. The maximum output power of 2.8 W at 1 030 nm was obtained with 800 μm SiC cooling, the output power has increased by 40% than that obtained with direct water cooling. The initial transmission of Cr4+:YAG crystal and the output coupling rate were optimized by Degnan′s theory. With the initial transmission of Cr4+:YAG crystal of 93% and the output coupling rate of 10%, a stable pulse train of 1.95 W averaged output power with a pulse energy of 1.2 mJ and pulse width of 74 ns were obtained with 800 μm SiC cooling. The repetition rate is 1.6 kHz, the slope efficiency is 18.1%, and the beam quality M2x=1.622, M2y=1.616.