The purpose of this paper is to analyze an efficient method for the solution of the nonlinear system resulting from the discretization of the elliptic Monge-Ampère equation by a Co interior penalty method with Lagrange finite elements.We consider the two-grid method for nonlinear equations which consists in solving the discrete nonlinear system on a coarse mesh and using that solution as initial guess for one iteration of Newton’s method on a finer mesh.Thus both steps are inexpensive.We give quasi-optimal W1,∞ error estimates for the discretization and estimate the difference between the interior penalty solution and the two-grid numerical solution.Numerical experiments confirm the computational efficiency of the approach compared to Newton’s method on the fine mesh.