As an important multi-objective optimization algorithm, multi-objective evolutionary algorithm based on decomposition (MOEA/D) attracts more and more attention recently. In this paper, some methods inspired from quantum behavior are integrated in MOEA/D. A new algorithm, quantum-inspired MOEA/D (QMOEA/D), is proposed and proved to be effective to improve the performance of MOEA/D. In the new algorithm, a global solution (GS) and a local solution (LS) are stored for each subproblem. The attractor and characteristic length in quantum-inspired method are designed with GS and LS. The LS is selected as the attractor for each subproblem. And the characteristic length is associated with the difference between the LS and GS. The algorithm based on nondominated sorting is used for comparing firstly. Then the original and some advanced versions of MOEA/D are used as the comparison algorithms. Through the comparison it can be found that GS and LS are helpful to retain the diversity of the solutions. A wide Pareto front can be obtained on most of the test suites. And the quantum-inspired generator is effective to obtain better solutions with GS and LS.