A high-power fiber laser amplifier with a laser wavelength of about 1060 to 1100 nm and an average laser power of more than about 500 W and an almost diffraction-limited beam quality (M.sup.2<1.5) comprises a double-clad laser fiber that has a separate, laser-active fiber core with an outer diameter of at least 20 .mu.m and a pump core that surrounds the fiber core and has an outer diameter of at least 50 .mu.m, and ytterbium-doped solid state laser that emits pump light with a wavelength of approximately 1030 nm, a beam quality of M.sup.2< of approximately 30 and a laser power of at least approximately 600 watts, for pumping the double-clad laser fiber.