Human DNA topoisomerases (topos) have been recognized as a good target molecule for the development of anticancer drugs because they play an important role in solving DNA topological problems caused by DNA strand separation during replication and transcription. In this study, we designed and synthesized 11 novel chromone backbone compounds possessing epoxy and halohydrin substituents with chirality. In the topos inhibition test, compounds 2, 9, 10, and 11 showed comparable topo I inhibitory activity at concentration of 100 μM compared to camptothecin, and all of the synthesized compounds showed moderate topo IIα inhibitory activity. Among them, compounds 9, 10 and 11 were more potent than the others in both topo I and IIα inhibitory activity. Compound 11 showed the most potent cell antiproliferative activity against all tested cancer cell lines with particularly strong inhibition (an IC 50 of 0.04 µM) of K562 myelogenous leukemia cancer cell proliferation. In the brief structure-activity relationship analysis, there was no clear correlation between stereochemistry and topos inhibitory and cytotoxic activity. 5(R),7(S)-bisepoxy-substituted compound 11 was the most potent DNA cross-linker and induced G2/M arrest in a cell cycle assay in a dose- and time-dependent manner. After the treatment time period induced apoptosis in K562 cells without increasing G2/M-phase cells. Overall, compound 11 showed good consistent inhibitory biological activity related to cancer cell proliferation.