Block copolymers with repulsive sub-chains form a variety of domain structures called microphase-separated structures. Most microphase-separated structures have a periodic patterned structure while in a stable state. On the other hand, metastable states with an acyclic structure and sufficiently long lifetimes are often observed around the configuration space of the periodic structures. In this study, we focused on the double gyroid structure—a type of microphase-separated structure—and built a model to predict free energy using topological data analysis (TDA), which has recently proven useful for analyzing acyclic compound structures such as the amorphous structure of glass. The model obtained can predict the free energy of the metastable state of the double-gyroid structure using persistent homology, which is one of the features of TDA.