This study investigates efficacy of cognitive biases for grammar acquisition. We present a simulation of virtual block world where a pair of a parent and an infant agent resides. When a parent takes an action and utters corresponding sentence, an infant guesses the meaning of the utterance from the situational change caused by the action. The infant tries to acquire a compositional grammar through an amount of utterances, and the grammar would be polished through generations. Through this process, we focus on how the symmetry and mutual exclusivity biases help this grammar refinement. We expect that the symmetry bias works to combine a situational change and an utterance, and that the mutual exclusivity bias contributes to solve the ambiguity between a situational change and an action; when the infant finds an utterance is already combined with a different meaning, he/she ignores the new pair of utterance/meaning by the latter bias.