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The recent demonstration of thermal conductivity of rough electrolessly etched Si nanowire (Hochbaum et al., Nature, 451:163, ) attracted a lot of interest, because it could not be explained by the existing theory; thermal conductivity of rough Si nanowires falls below the boundary scattering of the thermal conductivity. However, nanoscale pores presented in the nanowires (Hochbaum et al., Nano Letters, 9:3550-3554, ) hinder one to be fully convinced that the surface roughness solely made a contribution to the significant reduction in thermal conductivity. In this study, we synthesized vapor-liquid-solid (VLS) grown rough SiGe nanowire and measured and theoretically simulated thermal conductivity of the nanowire. The thermal conductivity of rough SiGe nanowire is an order of magnitude lower than that of bulk SiGe and around a factor of four times lower than that of smooth SiGe nanowire. This significant reduction could be explained by the fact that the surface roughness scatters medium-wavelength phonons, whereas the long-wavelength phonons are scattered by phonon boundary scattering, and the short-wavelength phonons are scattered by alloy scattering. [ABSTRACT FROM AUTHOR]