A die-casting machine using an electric servo motor as a driving source for injecting/filling molten metal into a cavity of a mold through an injection sleeve. The molten metal in the injection sleeve is injected/filled into the cavity by an injection member. During the course between the stage when the molten metal has not reached a gate of the mold yet and the stage when the molten metal begins to pass the gate of the mold, the speed of the injection member is controlled to be accelerated in a smooth speed characteristic curve which does not have a broken-line characteristic. Thus, rising to a high injection speed can be attained rapidly and smoothly.