Disc accretion to a rotating star with a non-dipole magnetic field is investigated for the first time in full three-dimensional magnetohydrodynamic simulations. We investigated the cases of (1) pure dipole, (2) pure quadrupole, and (3) dipole plus quadrupole fields. The quadrupole magnetic moment D is taken to be parallel to the dipole magnetic moment μ, and both are inclined relative to the spin axis of the star Ω. at an angle Θ. Simulations have shown that in each case the structure of the funnel streams and associated hotspots on the surface of the star have specific features connected with the magnetic field configuration. In the pure dipole case, matter accretes in two funnel streams which form two arch-like spots near the magnetic poles. In the case of a pure quadrupole field, most of the matter flows through the quadrupole ‘belt’ forming a ring-shaped hot region on the magnetic equator. In the case of a dipole plus quadrupole field, magnetic flux in the Northern magnetic hemisphere is larger than that in the Southern magnetic hemisphere, and the quadrupole belt and the ring are displaced to the south. The stronger the quadrupole, the closer the ring is to the magnetic equator. At sufficiently large Θ, matter also flows to the south pole, forming a hotspot near the pole. The light curves have a variety of different features which makes it difficult to derive the magnetic field configuration from the light curves. There are specific features which are different in cases of dipole- and quadrupole-dominated magnetic field: (1) angular momentum flow between the star and disc is more efficient in the case of the dipole field; and (2) hotspots are hotter and brighter in the case of the dipole field because the matter accelerates over a longer distance compared with the flow in a quadrupole case.