In this paper, we propose an algorithm for solving the generalized Nash equilibrium for noncooperative games by means of the quasi variational inequality. Incorporating the inertial steps to a projection-like method, we show the convergence of the generated sequence to the solution of a quasi-variational inequality, and hence the Nash equilibrium. We also implement the algorithm to some test problems, where the numerical experiment portrays that the convergence of our proposed algorithm is about twice as fast compared to the known projection-like method without the inertial steps.