In this study, we propose a new numerical technique to couple non-ordinary state-based peridynamics (NOSB-PD) and the finite element method (FEM), and improve the scheme by implementing an effective boundary imposition method and a stabilization method. This coupling scheme takes the mutual advantages of peridynamics and the FEM to solve fracture problems without the imposition of additional criteria, yielding enhanced computational efficiency. In addition, the coupling model brings the reduction of the boundary effect using the boundary imposition method. To combine the peridynamics and FEM, the model is partitioned into the peridynamic subregion and finite element subregion. Subsequently, the two subregions are bridged by interface elements, where peridynamic nodes are embedded. Two types of coupling schemes are developed and the boundary effect of the peridynamic subregion is analyzed in each coupling approach. Moreover, stabilization of the coupling method is implemented to control the zero-energy mode inherent in NOSB-PD to simulate fracture problems. The proposed methodology is verified by solving several quasi-static problems in the one- and two-dimensional domains, and fracture problems are solved. The crack paths predicted by the proposed coupling method are in good agreement with the results of the exact solution and the experiments.