Open vehicle routing problem is a kind of special vehicle routing problem, in which the vehicles do not return the depots after completing the task. Aiming at open vehicle routing problem, the mathematical model was founded by introducing virtual depots. A quantum evolutionary algorithm combined with local optimization algorithms was proposed in this paper, in which 0-1 matrix encoding was used to construct chromosomes, rotation gate with adaptively adjusting rotation angle was used to realize evolution, nearest neighbors and 2-Opt were incorporated to further improve solutions. Based on benchmark problems, the algorithm’s parameters were discussed, and the computation result was compared to those of other algorithms. The Computation results indicated that the proposed algorithm was an efficient method for solving open vehicle routing problem.