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It is well known that the symmetry bias greatly accelerates vocabulary learning. In particular, the bias helps infants to connect objects with their names easily. However, grammar learning is another important aspect of language acquisition. In this study, we propose that the symmetry bias also helps to acquire grammar rules faster. We employ the Iterated Learning Model, and revise it to include the symmetry bias. The result of the simulations shows that infants could abduce the meanings from unrecognized utterances using the symmetry bias, and acquire compositional grammar from a reduced amount of learning data.