In recent years, the interaction force between a permanent magnet and a closed superconductor coil has been gradually investigated in depth. The principle and application potential of an energy storage/convertor composed of a magnet and a closed superconducting coil have been proved. However, the study on the force between a magnet and a non-closed superconducting coil (superconducting roll stack) has hardly been reported in previous literature. The behavior of this kind of interaction and its influence to the interaction force between a permanent and a closed superconducting coil are also still unclear. In this paper, first we investigated the interaction force between a magnet and a superconducting roll stack. Then, a series of experiments were designed and conducted to clarify the factors affected the interaction force, including the geometrical parameters of the superconducting roll stack and the magnetic field density at the roll stack. Moreover, the comparison of the interaction forces between the magnet and roll stack or a closed coil was also introduced.