It is well known that the symmetry bias much accelerates the process of vocabulary learning, especially in infants' first language acquisition where they easily tend to connect objects with their names. However, the grammar learning is another important aspect of language acquisition. In this study, we contended that the symmetry bias also would help to learn grammar rules. We employed Kirby's model (Iterated Learning Model; ILM) in which the parental speakers uttered sentences with their semantic representaions and children guessed the background grammar in their minds; in turn, children became new parents and generated sentences in the following generation. We revised this model to include utterances without semantics. We have shown that children could abduce the meanings from utterances by the symmetry bias, and that they acquired the same language with smaller number of learning data by computer simulation.