The design of unstable resonator has carried out by Nd:GGG. Coupling system is optimistically designed to get the uniform of gain distribution to 94%. Thermal simulation module is established and temperature-distribution of laser medium is calculated. The simulation module is attested by the experimental results. Then the design parameters of unstable resonator are optimized by theoretically analytical module of unstable resonator. The experimental results show that the output power is more than 10 kW and the average beam quality is 5.84 times diffraction limit.