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The effect of phonon-interface scattering on the percolation of the phonon thermal conductivity in random nanowire composites is investigated by solving the phonon Boltzmann transport equation using the Monte Carlo simulation. The forming of a geometric percolating network does not lead to dramatic increase of the thermal conductivity in nanowire composites because of the dominance of the phonon-interface scattering. The thermal conductivity of nanocomposites is much less sensitive to the thermal conductivity contrast ratios of the constituent materials than that of bulk composites, especially when the volumetric concentration of the high thermal conductivity constituent is below the percolation threshold.