The nuclear structure of neutron-rich nuclei near the doubly-magic 132Sn is of high interest for both nuclear physics and nuclear astrophysics. Research on nuclear structure properties in this nuclear region will provide reliable groundwork for further investigations of ultra-neutron-rich nuclear structure and new physics in the neutron drip-line region. Until now, only scarce experimental data are available for this nuclear region, and theoretical research on nuclear structure has a great demand for a suitable Hamiltonian. In the present work, the crucial monopole corrections have been found. Reliable explanations of both low-lying levels and core excitations have been shown for nuclei in the A≈130 mass region. Furthermore, level inversion in low-lying states is predicted in the whole region.