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In this paper, we develop a robust weak Galerkin discretization for the incompressible miscible displacement problem in porous media, which is a nonlinear time-dependent system. The scheme we constructed is positive definite and flexible by arbitrarily shaped polygonal mesh without imposing extra conditions on the stabilization. The other feature of our method is that there is no limitation on the ratio of time-step and spatial mesh size. Error estimates are derived for concentration and pressure in the L 2 norm and energy norm, respectively. Extensive numerical experiments, including realistic test cases, have been conducted to verify our theoretical results and the efficiency of the method. [ABSTRACT FROM AUTHOR]