According to the infinite representation of the scaled boundary finite element method (SBFEM), an isogeometric scaled boundary finite element method (IGA-SBFEM) using the non-uniform rational B-splines (NURBS) is presented for the numerical solution of seepage problems in the unbounded domain. Further, the proposed method is extended to the modeling of seepage problems considering the parallel semi-infinite side-faces in the multilayered media. The proposed formulation is based on the SBFEM that only requires boundary discretization of the analyzed domain. And it advances the SBFEM by using the NURBS basis functions to exactly represent the geometry of the boundary and to approximate the solutions fields at the boundary. Thus, the proposed method fits neatly with the Boundary Representations (B-Reps) technique provided completely by CAD. The rigid tensor product structure can be reduced by one, since only the boundary information of the analyzed domain is required in the proposed approach. The method enhances the flexibility for describing complex geometry and offers many key improvements in comparison to the conventional SBFEM. Finally, the results from numerical examples are compared with the analytical solutions or reference solutions, illustrating the superiority of the proposed formulation.