Thickness effects on thermal conductivities of black phosphorus nanosheets, which are anisotropic in the zigzag and armchair planar directions, are experimentally and theoretically investigated in the thickness range of 13 to 48 nm. The thermal conductivities decrease with the thickness, decreasing from 13 to 8 W m-1 K-1 in the zigzag direction and from 10 to 6 W m-1 K-1 in the armchair direction at 300 K, respectively. The anisotropic thermal conductivities, regardless of the thickness, might result from the anisotropic phonon velocity arising from the hinge-like structure. The surface-driven suppression of the thermal conductivities at a nanometer scale is remarkable for a wide temperature range of 100 to 300 K due to phonon-boundary scattering, while the thermal conductivity becomes less dependent on the thickness at higher temperatures above 300 K, owing to the dominant phonon-phonon scattering.