For the conduction cooled end-pumped zig-zag slab module, a novel 10 kW high power laser amplifier setup of the all-solid slab laser has been designed. The laser extractive efficiency of the amplifier with various laser power densities and various incidence angles is simulated with a laser amplifier model. The optical-optical conversion efficiency of the laser amplifier is measured in the experiment. The experimental result agrees well with the simulation. A seed laser is amplified in a pre-amplifier stage and two amplifier stages all-solid-state amplifier system with high power and high beam quality to a output power of 11.3 kW, with the beam quality 7.56 times diffraction limit and the runtime over 110 seconds. The optics-optics conversion efficiency is 30%.