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. The 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. (C) 2002 American Institute of Physics.