Multi-scale quantum harmonic oscillator algorithm (MQHOA) is a novel global optimization algorithm inspired by wave function of quantum mechanics. In this paper, a MQHOA with individual stabilization strategy (IS-MQHOA) is proposed utilizing the individual steady criterion instead of the group statistics. The proposed strategy is more rigorous for the particles in the energy level stabilization process. A more efficient search takes place in the search space made by the particles and improves the exploration ability and the robustness of the algorithm. To verify its performance, numerical experiments are conducted to compare the proposed algorithm with the state-of-the-art SPSO2011 and QPSO. The experimental results show the superiority of the proposed approach on benchmark functions.