A carbon electrode grinding apparatus for shaping a front end of an arc discharge carbon electrode is provided with front end grinding blades configured to grind a front end surface of the carbon electrode, lateral surface grinding blades configured to grind a surface from the front end surface to a base end of the carbon electrode, and rotation means configured to rotate and drive the front end grinding blades and the lateral surface grinding blades around a rotation axis line coincident with an axis line of the carbon electrode.