A series of novel acridine N-acylhydrazone derivatives have been synthesized as potential topoisomerase I/II inhibitors, and their binding (calf thymus DNA—ctDNA and human serum albumin—HSA) and biological activities as potential anticancer agents on proliferation of A549 and CCD-18Co have been evaluated. The acridine-DNA complex 3b (-F) displayed the highest Kb value (Kb = 3.18 × 103 M−1). The HSA-derivatives interactions were studied by fluorescence quenching spectra. This method was used for the calculation of characteristic binding parameters. In the presence of warfarin, the binding constant values were found to decrease (KSV = 2.26 M−1, Kb = 2.54 M−1), suggesting that derivative 3a could bind to HSA at Sudlow site I. The effect of tested derivatives on metabolic activity of A549 cells evaluated by the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide or MTT assay decreased as follows 3b(-F) > 3a(-H) > 3c(-Cl) > 3d(-Br). The derivatives 3c and 3d in vitro act as potential dual inhibitors of hTopo I and II with a partial effect on the metabolic activity of cancer cells A594. The acridine-benzohydrazides 3a and 3c reduced the clonogenic ability of A549 cells by 72% or 74%, respectively. The general results of the study suggest that the novel compounds show potential for future development as anticancer agents.