A beveling machine to process a weld bead surface, which is capable of controlling the depth of bevel cut by a one-touch operation, the beveling machine comprising: a beveling machine body, wherein a spline shaft connection unit is positioned at an upper center part of the beveling machine body and a cutter operation unit is positioned at a lower center part thereof, and the spline shaft connection unit and the cutter operation unit are operatively connected to each other; a movable spline shaft vertically movably connected to the spline shaft connection unit by a screw, wherein a first spline is positioned around an upper outer circumference of the movable spline shaft; a bevel cut depth controlling unit, wherein a second spline surrounding an outside of the movable spline shaft is positioned around an inner circumference of the bevel cut depth controlling unit, moves by a vertical sliding motion and is connected to the first spline by a spline; a spring housing inserted into a guide groove formed at an upper part of the bevel cut depth controlling unit and integrally attached to an upper end of the movable spline shaft; an elastic spring interposed between an inner surface of the spring housing and the guide groove of the bevel cut depth controlling unit; a plurality of securing openings formed at a lower part of the bevel cut depth controlling unit in a circumferential direction; a plurality of location setting pins positioned at an upper outer part of the spline shaft connection unit in a circumferential direction and selectively fit into the securing openings, to fix the location of the bevel cut depth controlling unit and maintain the locking thereof; a sleeve shaft rotatably installed in the movable spline shaft; a movable cutter shaft rotatably installed in a bearing housing installed to be inserted into a lower part of the cutter operation unit, wherein the movable cutter shaft is integrally connected to a lower end of the sleeve shaft so that the movable cutter shaft and the sleeve shaft operatively rotate and vertically move together, and a spiral bevel gear inserted outside the movable cutter shaft and connected to a third spline positioned at the movable cutter shaft by a spline, to transmit the rotation power of a power shaft to the movable cutter shaft. a beveling machine body, wherein a spline shaft connection unit is positioned at an upper center part of the beveling machine body and a cutter operation unit is positioned at a lower center part thereof, and the spline shaft connection unit and the cutter operation unit are operatively connected to each other; a movable spline shaft vertically movably connected to the spline shaft connection unit by a screw, wherein a first spline is positioned around an upper outer circumference of the movable spline shaft; a bevel cut depth controlling unit, wherein a second spline surrounding an outside of the movable spline shaft is positioned around an inner circumference of the bevel cut depth controlling unit, moves by a vertical sliding motion and is connected to the first spline by a spline; a spring housing inserted into a guide groove formed at an upper part of the bevel cut depth controlling unit and integrally attached to an upper end of the movable spline shaft; an elastic spring interposed between an inner surface of the spring housing and the guide groove of the bevel cut depth controlling unit; a plurality of securing openings formed at a lower part of the bevel cut depth controlling unit in a circumferential direction; a plurality of location setting pins positioned at an upper outer part of the spline shaft connection unit in a circumferential direction and selectively fit into the securing openings, to fix the location of the bevel cut depth controlling unit and maintain the locking thereof; a sleeve shaft rotatably installed in the movable spline shaft; a movable cutter shaft rotatably installed in a bearing housing installed to be inserted into a lower part of the cutter operation unit, wherein the movable cutter shaft is integrally connected to a lower end of the sleeve shaft so that the movable cutter shaft and the sleeve shaft operatively rotate and vertically move together, and a spiral bevel gear inserted outside the movable cutter shaft and connected to a third spline positioned at the movable cutter shaft by a spline, to transmit the rotation power of a power shaft to the movable cutter shaft.