Nanofibrous materials containing the antitumor drug doxorubicin hydrochloride (DOX) were easily prepared using a one-step method by electrospinning of DOX/poly(L-lactide-co-D,L-lactide) (coPLA) and DOX/quaternized chitosan (QCh)/coPLA solutions. The pristine and DOX-containing mats were characterized by ATR-FTIR and X-ray photoelectron spectroscopy (XPS). The release rate of DOX from the prepared fibers increased with the increase in DOX content. The DOX release process was diffusion-controlled. MTT cell viability studies revealed that incorporation of DOX and QCh in the nanofibrous mats led to a significant reduction in the HeLa cells viability. It was found, that the antitumor efficacy of the DOX-containing mats at 6 h was higher than that of the free DOX. SEM, TEM, and fluorescence microscopic observations confirmed that the antitumor effect of QCh-based and DOX-containing fibrous mats was mainly due to induction of apoptosis in the HeLa cells.