High-pressure die-casting is a casting process in which is pressed the molten metal into a mold at high speed and high pressure. Hence it causes the gas to be entrained in the molten metal within the shot sleeve, the runner, and the product part, resulting in gas defects. Therefore, casting engineers to design an exhaust runner and overflow, called an exhaust system, to discharge the gas or gas-entrained molten metal outside of the mold completely. Besides, an overflow has a broader designable area than an exhaust runner. Hence it can discharge gas-entrained molten metal, which an exhaust runner cannot discharge. Therefore, designing an overflow with appropriate positions and volumes is important to discharge the gas more. In recent research, the system automatically designs overflow positions has been developed by combining optimization theory and computational fluid dynamics (CFD). However, only designing the overflow positions may cause gas defects by needing more overflow volume and unnecessary discharge of the molten metal. Furthermore, the calculation time will be much longer if the analysis area includes the entire mold. Therefore adapting the system to the complex shape of the product is difficult. In this research, we develop a system that designs the overflow positions and volume considering the direction of molten metal flow to discharge the gas-entrained molten metal completely. Finally, we conducted an actual die-casting experiment to verify the effectiveness of our proposed system.