This paper proposes a parallel quantum evolutionary algorithm (PQEA) using Client-Server model for multi-objective optimization problems. Firstly, the PQEA uniformly decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems. All the sub-problems are classified into several groups according to their similarities. Each "Client" processes the evolution for a group of neighbor sub-problems in parallel. There is a quantum individual used to address the sub-problems of a group in a "Client". Since the quantum individual is a probabilistic representation, it can share evolutionary information of the neighbor sub-problems in one group, while the sub-problems are orderly solved using a same q-bit individual. The "Server" maintains non-dominated solutions that are generated by every "Client". The current best solution for each sub-problem can be found in the "Server", when the quantum individual updated its states for evolution. Experimental results have demonstrated that PQEA obviously outperforms the most famous multi-objective optimization algorithms MOEA/D on the bi-objectives. For the more objectives, the PQEA obtains the similar results with MOEA/D, even with the same evaluation times. Furthermore, in this paper, the scalability and sensitivity of PQEA have also been experimentally investigated.