A novel series of 35 angularly fused pentacyclic 13H-benzo[f]chromeno[4,3-b][1,7]naphthyridines and 13H-benzo[f]chromeno[4,3-b][1,7]naphthyridin-5-ium chlorides were designed and synthesized. Their cytotoxic activities were investigated against six human cancer cell lines (NCIH23, HCT15, NUGC-3, ACHN, PC-3, and MDA-MB-231). Among all screened compounds; 28, 30, 34, 35, 46, 48, 52, and 53 compounds exhibited potent cytotoxic activities against all tested human cancer cell lines. Further, these potent lead cytotoxic agents were evaluated against human Topoisomerase I and IIα inhibition. Among them, the compound 48 exhibited dual Topoisomerase I and IIα inhibition especially at 20 μM concentrations the compound 48 exhibited 1.25 times more potent Topoisomerase IIα inhibitory activity (38.3%) than the reference drug etoposide (30.6%). The compound 52 also exhibited excellent (88.4%) topoisomerase I inhibition than the reference drug camptothecin (66.7%) at 100 μM concentrations. Molecular docking studies of the compounds 48 and 52 with topo I discovered that they both intercalated into the DNA single-strand cleavage site where the compound 48 have van der Waals interactions with residues Arg364, Pro431, and Asn722 whilst the compound 52 have with Arg364, Thr718, and Asn722 residues. Both the compounds 48 and 52 have π-π stacking interactions with the stacked DNA bases. The docking studies of the compound 48 with topo IIα explored that it was bound to the topo IIα DNA cleavage site where etoposide was situated. The benzo[f]chromeno[4,3-b][1,7]naphthyridine ring of the compound 48 was stacked between the DNA bases of the cleavage site with π-π stacking interactions and there were no hydrogen bond interactions with topo IIα.