The multiobjective evolutionary algorithm based on decomposition(MOEA/D) selects next generation without considering the distance between solutions and subproblems, which may yield a result of poor diversity. Therefore, the MOEA/D with bigraph matching(MOEA/D-BM) is proposed. The algorithm models the relationship between solutions and subproblems through bigraph matching, and thus improves the performance of the algorithm by considering the convergence and diversity simultaneously in next generation selection. The experimental results on a variety of test instances show that the proposed algorithm is effective in comparison with 3 state-of-the-art decomposition-based multiobjective evolutionary algorithms.