To realize high-quality group gaming services, players’ gaming demands and computing tasks can be offloaded to edge servers through mobile edge computing, which can reduce response latency. However, how to achieve fairness in group gaming is an open problem. In this paper, we propose a solution to the above problem for a typical group gaming genre, namely Multi-player Online Battle Arena (MOBA). Firstly, we formulate the edge user allocation problem which needs to develop reasonable allocation strategies for players and offload their computing tasks to the appropriate edge server to improve their gaming experience. Secondly, we design a user allocation algorithm called MOBA-EUA. It’s a two-phase heuristic approach. In the first phase, players will be allocated to available edge servers that satisfy multiple constraints based on the principle of minimizing system responsiveness. Then they proactively perform reallocations to achieve inter-group fairness, until the grouping delay difference cannot be smaller. Finally, experimental results prove the effectiveness of our proposed algorithm.