PACS 71.35. Ji, 73.21.Fg We study the confinement of magnetoexcitons in quantum wells in the presence of a strong external homogeneous magnetic field and a cylindrical symmetric inhomogeneous magnetic field created by a superconducting disk, placed on the top of the well. We calculate numerically the trapping energy and the corresponding center-of-mass wave function of magnetoexcitons in a GaAs single quantum well. The calculations clearly indicate the formation of bound exciton states with nonzero values for the center-of-mass exciton wave function only in a sufficiently small area. This effect of exciton trapping can be used to design new functional nanoelectronic devices.