Personality has not only been studied at an individual level, its composite effect between team members has also been indicated to be related to the overall group performance. In this work, we propose a Personality Composite-Network (PCompN) architecture that models the group-level personality composition with its intertwining effect being integrated into the network modeling of team members vocal behaviors in order to predict the group performances during collaborative problem solving tasks. In specific, we evaluate our proposed P-CompN in a large-scale dataset consist of three-person small group interactions. Our framework achieves a promising group performance classification accuracy of 70.0%, which outperforms baseline model of using only vocal behaviors without personality attributes by 14.4% absolutely. Our analysis further indicates that our proposed personality composite network impacts the vocal behavior models more significantly on the high performing groups versus the low performing groups.