The invention relates to a gradient shield coil (5) for a MRI apparatus (1). The gradient shield coil (5) according to the invention comprises windings (6, 7) around its longitudinal axis (A), wherein at least one winding (7) is arranged as a meandering winding (7). This meandering winding (7) comprises multiple contiguous sections (8) along its circumference, wherein in each of these sections (8) a pair of conductor loops (9, 10) is provided in such a way that a current in the meandering winding (7) would run in opposite directions in the two conductor loops (9, 10). In this way, dissipation in the superconductive coils of a superconductive magnet (2) of a respective MRI apparatus (1) may be further reduced.