We report on the generation of kW-class, continuous-wave, radially polarized laser radiation in an Yb:LuAG thin-disk laser (TDL). Output powers of up to 980 W were achieved with optical efficiency of 50.5% with respect to the incident pump power of the TDL. The degree of radial polarization was measured to be 95.5% at maximum output power. This was achieved by the integration of a new generation of broadband, large-area grating-waveguide mirror with unprecedented high polarization discrimination as the end-mirror in the TDL resonator.