Previous studies have suggested that in emotionally-oriented communication such as counseling and casual conversation, non-verbal communication characteristics such as turn-taking and vocal pitch synchrony were related to formation of rapport. However, in cognitive goal-oriented communication such as group problem-solving, there are few studies investigating whether the features of non-verbal communication cues correlate with rapport. In this research, we focused on the turn-taking and vocal pitch synchrony during creative problem-solving communication, and investigated their possible relationship with rapport. We adopted the Alternative Uses Tasks (AUT) as the case of cognitive goal-oriented communication, which measures individual creativity, and reorganized it to a group communication task. In the experiment, groups of three people each with the same gender discussed ideas for unusual uses of daily necessities for 20 minutes. The number of utterances which were responsive to the utterance of other speaker was used as an indicator of turn-taking, and the mean value of difference of the vocal pitch between the participant's was used as an indicator of vocal pitch synchrony. Multiple regression analysis showed that turn-taking, rather than total utterances, were significantly positively correlated with rapport, while vocal pitch synchrony did not contribute to rapport explanations. The results suggest that in the creative problem-solving discussion, the more turn-taking the conversation has, the more you feel rapport. The discrepancy with the previous study may suggest that the vocal pitch synchrony contribute to rapport in emotionally-oriented communication, but the vocal pitch synchrony would be not so relevant in forming rapport in more cognitive goal-oriented communication. In conclusion, the amount of turn-taking is a reliable non-verbal predictor of rapport, even in cognitive goal-oriented communication.