Abstract: Based on the electric and magnetic current combined-field integral equation (JMCFIE), a fast algorithm is presented for calculating 3D scattering by large homogeneous objects. An efficient and flexible parallel implementation of the multilevel fast multipole algorithm (MLFMA) is employed to enhance efficiency and capability of the JMCFIE approach. This parallel approach is proposed by using open multi-processing(OpenMP) to further accelerate the pure MPI parallel MLFMA. This hybrid MPI-OpenMP paralleled MLFMA improves the load-balance and scalability by combing processes and threads flexibly, hence depress unavoidable load imbalance in the pure MPI parallel MLFMA. Numerical experiments on targets with different sizes including a dielectric sphere with radius 120 m modeled with about 110 million unknowns show the scalability and computational capability of the proposed MPI-OpenMP-MLFMA enhanced JMCFIE for extremely large targets.