This paper makes a full-scale introduction to the advancement of research on group mobility model and analyses characteristics and the application range of different models. Most of the existing group mobility models exhibit certain drawbacks in describing the group movement behaviors. A Gibbs sampler based simulated annealing group mobility (GGM) model is proposed to address this deficiency. By simulation comparison with reference point group mobility (RPGM) model, this paper analyzes the impact of two models on Ad Hoc network protocol performance. Experimental results show that the proposed GGM model can describe three different behaviors of group movements effectively, which are group gathering, dispersion, and linear formation, by choosing Gibbs potential functions. The simulation also indicates that different group mobility models have different impact on the performance evaluation of ad hoc network protocol.