A winding machine (1) for winding solenoid-shaped coils (21) with band-shaped conductors (6), comprising a winding means (3) which holds a circular-cylindrical coil core (2) of a coil (21) to be wound, and a winding drive which rotates a coil core (2), which is held in the winding means (3), about a winding axis W, wherein the winding means (3) can be moved in a first direction A by an axial drive, the direction A preferably extending approximately parallel to the winding axis W, is characterized in that the winding means (3) can be rotated about a pivot axis S by a pivot drive, wherein the pivot axis S extends perpendicularly to the direction A. The winding machine winds a solenoid-shaped coil with several layers of a band-shaped conductor without damaging the band-shaped conductor, in particular, when the band-shaped conductor contains brittle superconducting material.