The embodiment of the invention discloses a flame cutter machine with a micro-arc-shaped section, which comprises a bodywork, a synchronous clamping mechanism and a cutting gun travelling mechanism and also comprises a support, wherein the synchronous clamping mechanism and the cutting gun travelling mechanism are respectively arranged on the support; the synchronous clamping mechanism, the cutting gun travelling mechanism and the support are capable of sliding relative to the bodywork; the support is provided with an elongated regulation hole; and the support is arranged on the bodywork by aconnecting pin through the regulation hole. Before cutting is started, while a casting blank is clamped by a clamp in the synchronous clamping mechanism of the flame cutter machine, the support in the synchronous clamping mechanism is forced to be fixed relative to the casting blank so as to automatically center the relative position of a micro-arc-shaped guide rail in the cutting gun travelling mechanism to the casting blank by taking the side arc of the casting blank as the reference to achieve the goal of accurately cutting the casting blank by taking the side arc of the casting blank as the reference to form the micro-arc-shaped section.