Optimum conditions for production of semi-solid Al-Zn-Mg alloy billets was carried out by the Taguchi design method. And, Al-Zn-Mg alloy billets contained Sc (free, 0.1 and 0.3 mass %) were fabricated at optimum conditions. Evolution of microstructure in semi-solid state was investigated through various liquid fractions, holding times and holding temperatures. The Al-Zn-Mg alloy billets reheated at $615^{circ}C$ during 30min are grain growth and it was fractured due to increasing liquid fraction before quenching. And, during reheating up to $600^{circ}C$, grain growth of Al-Zn-Mg alloy billets contained Sc (0.1 and 0.3 mass %) was not occurred in comparison with those of Al-Zn-Mg alloy without Sc. It was thought that $Al_3Sc$ phases have a pinning effect in grain boundary and Sc content of 0.1 mass% is able to inhibit grain growth effectively through reheating process.