Abstract: A concurrent transmission scheme is proposed in this paper based on nodal SINR (Signal to Interference plus Noise Ratio) under fast and slow fading coexistence channel in Ad hoc networks. Based on the distribution of channel quality, a concurrent transmission model is given between different sources and destinations with non-cooperative game theory and Bayesian Nash Equilibrium. Then the relay mechanism is proposed to increase the concurrent transmission opportunity for hunger nodes whose channel qualities are under concurrent transmission threshold for a long time. Simulation results show that the proposed CTCG (Concurrent Transmission based on Channel quality with Game theory aid) model can greatly increase the chance of concurrent transmission, improve the system throughput and handle the hunger nodes transmission problems in Ad hoc networks.