A Quantum-inspired Migrating Birds Co-Optimization (QMBCO) algorithm was proposed for minimizing the makespan in Lot-streaming Flow shop Scheduling Problem (LFSP). Firstly, the quantum coding based on Bloch coordinates was applied to expand the solution space. Secondly, an initial solution improvement scheme based on Framinan-Leisten (FL) algorithm was used to makeup the shortage of traditional initial solution and construct the random initial population with high quality. Finally, Migrating Birds Optimization (MBO) and Variable Neighborhood Search (VNS) algorithm were applied for iteration to achieve the information exchange between the worse individuals and superior individuals in proposed algorithm to improve the global search ability. A set of instances with different scales were generated randomly, and QMBCO was compared with Discrete Particle Swarm Optimization (DPSO), MBO and Quantum-inspired Cuckoo Co-Search (QCCS) algorithms on them. Experimental results show that compared with DPSO, MBO and QCCS, QMBCO has the Average Relative Percentage Deviation (ARPD) averagely reduced by 65%, 34% and 24% respectively under two types of running time, verifying the effectiveness and efficiency of the proposed QMBCO algorithm.