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This paper presents a new multiobjective bio-inspired algorithm based on membrane computing (MOBIAMC). Similar to the single objective bio-inspired algorithm based on membrane computing (BIAMC), MOBIAMC has a netted membrane structure. Most rules are different from those used in BIAMC. The proposed algorithm applies no operation on keeping the uniformity and variety of candidate solution set or non-dominate solution set in the process of approaching to the true Pareto-optimal front due to its parallel and distributed computation. The comparisons with three multiobjective evolutionary algorithms illuminate that the proposed algorithm is simple and computes fast with high precision in approaching to the true Pareto-optimal fronts of eight benchmark multiobjective optimization functions.