Abstract: Flow shop scheduling problem (FSP) widely exists in enterprise production processes. Optimal scheduling method can improve productivity and reduce production cost. In this paper, an optimization algorithm based on the chaotic quantum behaved particle swarm is proposed to solve the permutation flow shop scheduling problem, in which the chaotic mechanism is introduced into quantum behaved particle swarm optimization (QPSO) such that the shortcoming of easily falling into local minimum for QPSO can be avoided. Meanwhile, the fast convergence speed of QPSO can be kept in this proposed algorithm. Besides, a new representation scheme is proposed to overcome the difficulties of conversion from chaotic variable into job sequence. The simulation results verify the effectiveness of the proposed algorithm in this work.