We report the As-75-NMR study on a single crystal of the hole-doped iron-pnictide superconductor Ba0.72K0.28Fe2As2 (T-c = 31.5 K). We find that the Fe antiferromagnetic spin fluctuations are anisotropic and are weaker compared to underdoped copper-oxides or cobalt-oxide superconductors. The spin lattice relaxation rate 1/T-1 decreases below T-c with no coherence peak and shows a stepwise variation at low temperatures, which is indicative of multiple superconducting gaps, as in the electron-doped Pr(La) FeAsO1-xFx. Furthermore, no evidence was obtained for a microscopic coexistence of a long-range magnetic order and superconductivity. Copyright (C) EPLA, 2009