A plated steel sheet with a quasicrystal includes a steel sheet and a plated-metal-layer arranged on a surface of the steel sheet. The plated-metal-layer includes, as a chemical composition, Mg, Zn, and Al, and satisfies 25%≤Zn+Al in atomic %. The plated-metal-layer includes, as a metallographic structure, a quasicrystal phase. A Mg content, a Zn content, and an Al content in the quasicrystal phase satisfy 0.5≤Mg/(Zn+Al)≤0.83 in atomic %. In addition, an average equivalent circle diameter of the quasicrystal phase is larger than 1 μm and equal to or smaller than 200 μm.