A grinding machine (1) for grinding of a profile, comprising a machine bed (2), wherein a machining device (3) is arranged on the machine bed (2), wherein the machining device (3) comprises a swivel head (4) which carries a first grinding spindle (5) with a first grinding tool (6), especially with a roughing grinding tool, and a second grinding spindle (7) with a second grinding tool (8), especially with a finishing grinding tool, wherein a workpiece carrier being a rotary table (9) is arranged on the machine bed (2). To allow the production of workpieces with a complex geometry in a high precision in an economical manner the invention proposes that the swivel head (4) further carries at least one third grinding spindle (10) with a third grinding tool (11), wherein the swivel axle (A) of the swivel head (4) is directed horizontally and the axis of rotation (B) of the rotary table (9) is directed vertically.