Ligands that bind to and stabilize guanine-quadruplex (G4) structures to regulate DNA replication have therapeutic potential for cancer and neurodegenerative diseases. Because there are several G4 topologies, ligands that bind to their specific types may have the ability to preferentially regulate the replication of only certain genes. Here, we demonstrated that binding ligands stalled the replication of template DNA at G4, depending on different topologies. For example, naphthalene diimide derivatives bound to the G-quartet of G4 with an additional interaction between the ligand and the loop region of a hybrid G4 type from human telomeres, which efficiently repressed the replication of the G4. Thus, these inhibitory effects were not only stability-dependent but also topology-selective based on the manner in which G4 structures interacted with G4 ligands. Our original method, referred to as a quantitative study of topology-dependent replication (QSTR), was developed to evaluate correlations between replication rate and G4 stability. QSTR enabled the systematic categorization of ligands based on topology-dependent binding. It also demonstrated accuracy in determining quantitatively how G4 ligands control the intermediate state of replication and the kinetics of G4 unwinding. Hence, the QSTR index would facilitate the design of new drugs capable of controlling the topology-dependent regulation of gene expression.