<p>This paper addresses an indefinite linear-quadratic mean field games for stochastic large-population system, where the individual diffusion coefficients may depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. The authors employ a direct approach to derive the <i>ε</i>-Nash equilibrium strategy. First, the authors formally solve an <i>N</i>-player game problem within a vast but finite population setting. Subsequently, by introducing two Riccati equations, the authors decouple or reduce the high-dimensional systems to yield centralized strategies, which depend on the state of a specific player and the average state of the population. As the population size <i>N</i> goes infinity, the construction of decentralized strategies becomes feasible. Then, the authors demonstrate that these strategies constitute an <i>ε</i>-Nash equilibrium. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed strategies.</p>