We report an axion dark matter search at Dine-Fischler-Srednicki-Zhitnitskii sensitivity with the CAPP-12TB haloscope, assuming axions contribute 100% of the local dark matter density. The search excluded the axion-photon coupling g_{aγγ} down to about 6.2×10^{-16} GeV^{-1} over the axion mass range between 4.51 and 4.59 μeV at a 90% confidence level. The achieved experimental sensitivity can also exclude Kim-Shifman-Vainshtein-Zakharov axion dark matter that makes up just 13% of the local dark matter density. The CAPP-12TB haloscope will continue the search over a wide range of axion masses.