In a burr removing method and apparatus of the present invention, a burr located at an edge of a steel piece is cut with a cutter by disposing the cutter such that the flank of the cutter is substantially in parallel with the surface of the steel piece on which the burr exists and the angle between the cutting edge of the cutter and the edge of the steel piece which the burr intersects is at least 45° and relatively moving the cutter toward the outside of the steel piece along the lengthwise direction of the burr; or by disposing the cutter such that the flank of the cutter is substantially in parallel with the surface of the steel piece on which the burr exists and the angle between the cutting edge of the cutter and the edge of the steel piece which the burr intersects is at least 90° and cutting the burr located at the edge of the steel piece by relatively moving the cutter perpendicularly to the lengthwise direction of the burr. In the present invention, burrs such as welding burrs and the like formed when billets and so on are continuously rolled can be cut without the occurrence of a protruding burr.