Weighted linear scalar, which transfers a multi-objective problem to many single objective sub-problems, is a basic strategy in traditional multi-objective optimization. However, it is not well used in many multi-objective evolutionary algorithms because of most of them are lack of balancing between exploitation and exploration for all sub-problems. This paper proposes a novel multi-objective evolutionary algorithm called multi-objective quantum evolutionary algorithm (MOQEA). Quantum evolutionary algorithm is a recent developed heuristic algorithm, based on the concept of quantum computing. The most merit of QEA is that it has little q-bit individuals are evolved to obtain an acceptable result. MOQEA decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems and optimizes them simultaneously. Each sub-problem is optimized by one q-bit individual. The neighboring solutions that are defined as a set of non-dominated solutions of sub-problem are generated from the corresponding q-bit individual. The experimental results have demonstrated that MOQEA outperforms or performs similarly to MOGLS and NSGA-II on discrete multi-objective problems.