A nonlinear Finite Element formulation and a numerical methodology to model the nonlocal and nonlinear effects introduced by the tunneling effect conduction model within the polymer matrix bet- ween close graphene sheets is proposed, which could explain the percolation phenomenon and nonlinear electric behavior of graphene-reinforced nanocomposites with polymer matrix. The computed effective conductivity is evaluated over representative volumes containing arbitrary distributed graphene sheets. The effect of applied electric field, barrier height and graphene aspect ratio are analyzed