It has been widely observed that there exists no universal best Multi-objective Evolutionary Algorithm (MOEA) dominating all other MOEAs on all possible Multi-objective Optimization Problems (MOPs). In this work, we advocate using the Parallel Algorithm Portfolio (PAP), which runs multiple MOEAs independently in parallel and gets the best out of them, to combine the advantages of different MOEAs. Since the manual construction of PAPs is non-trivial and tedious, we propose to automatically construct high-performance PAPs for solving MOPs. Specifically, we first propose a variant of PAPs, namely MOEAs/PAP, which can better determine the output solution set for MOPs than conventional PAPs. Then, we present an automatic construction approach for MOEAs/PAP with a novel performance metric for evaluating the performance of MOEAs across multiple MOPs. Finally, we use the proposed approach to construct a MOEAs/PAP based on a training set of MOPs and an algorithm configuration space defined by several variants of NSGA-II. Experimental results show that the automatically constructed MOEAs/PAP can even rival the state-of-the-art ensemble MOEAs designed by human experts, demonstrating the huge potential of automatic construction of PAPs in multi-objective optimization.