We report, to the best of our knowledge, the highest power conductive-cooled active-mirror amplifier (CcAMA) using Yb:YAG with a pulse energy of 10 J. By using four liquid-nitrogen circulating cooled laser heads, we achieved a repetition rate, pulse energy, and average power of 33.3 Hz, 9.3 J, and 310 W, respectively. The problem of wavefront distortion, which is difficult to solve with a large-aperture active-mirror laser, is suppressed by using reinforcing materials with the same thermal expansion coefficient. We have confirmed that the wavefront distortion is small (0.15λ P-V per head) at 100 Hz operation, which paves the way for 100 Hz operation with the CcAMA concept.