A zinc-plated steel sheet with an ageing resistance is produced from an Al-killed steel by hot dip type, continuous zinc plating including recrystallization and annealing, where after recrystallization and grain growth, the steel sheet is quenched at a cooling rate of 30.degree..about.250.degree. C/sec from 720.degree..about.600.degree. C. to 310.degree..about.200.degree. C.; after keeping the steel sheet at the same temperature for 0 to 15 seconds, the steel sheet is reheated to a molten zinc bath temperature; then the steel sheet is dipped into the molten zinc bath for zinc-plating; and then the steel sheet is cooled at a cooling rate of 250 to 5.degree. C./sec from that temperature to 350.degree. C.; and then the steel sheet is cooled at a specific average cooling rate in a temperature region of 350.degree. C. to 300.degree. C. and at a specific average cooling rate in a temperature region of from 300.degree. C. to 285.degree..about.220.degree. C.