Vortex pinning in a type-II superconducting Pb film covering a Co/Pt multilayer with perpendicular magnetic anisotropy is investigated. Different stable magnetic domain patterns like band and bubble domains can be created in the Co/Pt multilayer, clearly influencing the vortex pinning in the superconducting Pb layer. Most effective pinning is observed for the bubble domain state. We demonstrate that the pinning properties of the superconductor/ferromagnet bilayer can be controlled by tuning the size, density and magnetization direction of the bubbles.Magnetic flux penetrates type-II superconductors in the form of quantized vortices, which have the tendency to form a periodic lattice. These vortices move when a current is sent through the superconductor, thus causing dissipation and limiting the critical current density j c of the superconductor. To enhance j c , vortex motion must be prevented. The latter can be achieved by introducing different pinning centers such as defects created by ion [1] or neutron irradiation [2], lithographically introduced holes [3,4,5], or magnetic dots [6,7,8,9].Recently it was proposed that vortices in a superconductor/ferromagnet (SC/FM) multilayer are strongly pinned if the FM has a stripe domain structure, which typically exists in thin magnetic films with perpendicular anisotropy [10]. Enhanced pinning was observed in SC/FM bilayers compared to SC reference films [11,12]. However, in these studies the domain structure of the FM was unknown. In this Letter, we systematically investigate the influence of the domains in a ferromagnetic Co/Pt multilayer with perpendicular anisotropy on a type-II superconducting Pb film grown on top of the FM. Stable domain structures can be produced in a controlled way by magnetizing the sample before measuring the superconducting properties of the Pb film. We show that the strongest vortex pinning is obtained when localized domains (bubble domains) are present in the FM, and that by changing size and density of the bubbles one can control and optimize the vortex pinning.The Co/Pt multilayer is deposited on a Si substrate with amorphous SiO 2 top layer in an MBE apparatus by e-beam evaporation. The multilayer has a [Co(0.4 nm)/Pt(1.0 nm)] 10 structure on a 2.8 nm Pt base layer. A 10 nm Ge film, a Pb film with thickness d P b = 50 nm and a 30 nm Ge capping layer are subsequently evaporated on the Co/Pt multilayer (see Fig. 1) at a substrate temperature of 77 K. The Pb film has a critical temperature of T c = 7.23 K. The penetration depth λ(0) = 42 nm and the coherence length ξ(0) = 41 nm are estimated from measurements of the temperature dependence of the upper critical field. The Ge film between Pb and Co/Pt is insulating at low temperatures, so that the proximity effects between Pb and Co/Pt are suppressed.The Co/Pt multilayer has perpendicular magnetic anisotropy [13], which is confirmed by hysteresis loop (Fig. 3). measurements using the magneto-optical Kerr effect (MOKE). Fig. 2 shows the magnetization M f m of the Co/Pt multilayer, normalized...