<p>In this paper, we propose and analyze a modified adaptive two-grid (MATG) finite element method (FEM) for nonsymmetric or indefinite elliptic problems. In this method, we need to solve an extra symmetric positive definite (SPD) residual equation and correct the solution in the previous step before solving the SPD approximate problem. We construct a new residual-based a posteriori error estimator and prove its reliability. We also prove the contraction of the quasi-error and the convergence of the modified algorithm. At last, we report some numerical results to show the effectiveness and robustness of the proposed method.</p>