Although large space structures(LSS) such as a space station, a solar power station satellite, etc., are theoretically distributed parameter and infinite-dimensional systems, they have to be modeled into a lumped parameter and large finite-dimensional system for control system design. Besides, there remains the fundamental problem that the modeled large finite-dimensional system must be controled with a much smaller dimensional controller due to the limitation of computing resources. This causes the spillover phenomenon which degrades control performances and reduces the stability margin. Furthermore, it may destabilize the entire feedback control system. In this paper, we propose a novel spillover suppression method in the active vibration control of large flexible structures by using eigenstructure assignment. Its validity and effectiveness are investigated and verified by the numerical experiments using a simply supported flexible beam, which is modeled to have four controlled modes and eight uncontrolled modes.