A continuous-wave-operation laser amplifier chain consisting of three multi-concentration-doped Yb:YAG slab gain modules (GMs) at room temperature is presented. The output power of 22.3 kW with the beam quality of 3.3 times the diffraction limit is achieved from this chain. To the best of our knowledge, based on a Yb:YAG slab at room temperature, the highest power to date while maintaining excellent beam quality laser output. An extraction efficiency of 36% from the single slab GM is obtained and can be further enhanced to 46% by optimizing the parameters of GM. These results have confirmed that the Yb:YAG slab has an excellent scaling performance and is suitable for the development of high-average-power lasers.