In a plasma cutting apparatus for cutting a workpiece with a plasma arc, a cutting torch moves relative to the workpiece. The cutting torch produces plasma arc in accordance with a cutting current supplied thereto. To improve surface roughness of the cut facet of the workpiece, a pulsating current is superimposed on a D.C. current to provide the cutting current, wherein the frequency of the pulsating current is controlled in accordance with the moving speed of the cutting torch.