The human telomere region is known to contain guanine-rich repeats and form a guanine-quadruplex (G4) structure. As telomeres play a role in the regulation of cancer progression, ligands that specifically bind and stabilize G4 have potential therapeutic applications. However, as the human telomere sequence can form G4 with various topologies due to direct interaction by ligands and indirect interaction by the solution environment, it is of great interest to study the topology-dependent control of replication by ligands. In the present study, a DNA replication assay of a template with a human telomere G4 sequence in the presence of various ligands was performed. Cyclic naphthalene diimides (cNDI1 and cNDI2) efficiently increased the replication stall of the template DNA at G4 with an anti-parallel topology. This inhibition was stability-dependent and topology-selective, as the replication of templates with hybrid or parallel G4 structures was not affected by the cNDI and cNDI2. Moreover, the G4 ligand fisetin repressed replication with selectivity for anti-parallel and hybrid G4 structures without stabilization. Finally, the method used, referred to as quantitative study of topology-dependent replication (QSTR), was adopted to evaluate the correlation between the replication kinetics and the stability of G4. Compared to previous results obtained using a modified human telomere sequence, the relationship between the stability of G4 and the effect on the topology-dependent replication varied. Our results suggest that native human telomere G4 is more flexible than the modified sequence for interacting with ligands. These findings indicate that the modification of the human telomeric sequence forces G4 to rigidly form a specific structure of G4, which can restrict the change in topology-dependent replication by some ligands.