<p>For the substation WAPI networks, there are a large number of mobile terminals, which often roam to some different access points (APs). Faced with these APs, each terminal has to solve such a problem: how to select the optimal AP for the highest transmission rate? Centralized allocation approaches require high computational complexity. Consequently, they cannot quickly adapt to dynamic environments. Hence, the evolutionary game model (EGM), which guides each terminal to select its optimal AP in a distributed manner, is suitable for the dynamic environment. However, the traditional EGM requires a long convergence time to derive the equilibrium solution. To shorten this convergence time, in this paper, we propose a novel fast-convergence evolutionary game model (FCEGM), which includes two probabilities for the mobile terminal’s AP selection in the substation WAPI networks. First, each terminal randomly selects an initial AP and constructs two probabilities (i.e., the determine-probability and transfer-probability). Second, based on the determine-probability, each terminal determines whether to reselect another AP. Third, based on the transfer-probability, this terminal decides which AP to reselect. Finally, after several iterations, the FCEGM still derives a unique and stable equilibrium solution. Among two probabilities, the transfer-probability distributes many terminals over several dominant APs but does not concentrate them on the most dominant AP, which reveals the FCEGM’s novelty. Simulation results demonstrate that the proposed FCEGM reduces the convergence time by over 40% compared to the traditional EGM.</p>