This paper presents the global-local finite cover method (GL-FCM) that is capable of analyzing structures involving local heterogeneities and propagating cracks. The suggested method is composed of two techniques. One of them is the FCM, which is one of the PU-based generalized finite element methods, for the analysis of local cohesive crack growth. The mechanical behavior evaluated in local heterogeneous structures by the FCM is transferred to the overall (global) structure by the so-called mortar method. The other is a method of mesh superposition for hierarchical modeling, which enables us to evaluate the average stiffness by the analysis of local heterogeneous structures not subjected to crack propagation. Several numerical experiments are conducted to validate the accuracy of the proposed method. The capability and applicability of the proposed method is demonstrated in an illustrative numerical example, in which we predict the mechanical deterioration of a reinforced concrete (RC) structure, whose local regions are subjected to propagating cracks induced by reinforcement corrosion.