We describe the magnetic shielding system of the neutron-antineutron oscillation experiment at the ILL, Grenoble. It shields the cold neutron free flight path over a volume of 75 m length and 1 m diameter against external magnetic fields. With a field suppression factor of approximately 10(4), the mean residual magnetic field along the beam is well below 10 nT, which corresponds to a quasi-free neutron propagation efficiency of better than 99%.