A mobile rail grinding machine comprises a machine frame mounted on the rails of a track for continuously moving in the direction of, and along, the track, a tool carrier frame vertically adjustably mounted on the machine frame, a rail grinding tool or a group of such tools mounted on the carrier frame for vertical adjustment in a direction vertical to the machine frame to press the tool or tools against surface areas of the rails to grind irregularities off the surface areas, and a drive for imparting to the tool carrier frame a reciprocating working movement in the direction of the track independent of, and additional to, that simultaneously imparted to it by the movement of the machine frame. The invention also is directed to a rail grinding method wherein the rail is ground by such a compound working movement.