The behaviour of the magnetic field inside the superconducting quark matter core of a neutron star is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate field to the usual magnetic and to the gluomagnetic gauge fields. We solve the problem for three different physical situations: a semi-infinite region with a planar boundary, a spherical region, and a cylindrical region. We show that Meissner currents near the quark core boundary effectively screen the external static magnetic field.