Electrospun composite nanofibrous scaffolds have attracted much interest for use as drug delivery vehicles in recent years. Herein, we attempted to first encapsulate the anticancer drug doxorubicin (DOX) using inorganic rod-like nano-hydroxyapatite (n-HA) as a carrier. Then, the DOX-loaded n-HA particles were mixed with poly(lactic-co-glycolic acid) (PLGA) solution to fabricate electrospun hybrid nanofibers. The formation of drug–n-HA complexes and the drug-loaded composite nanofibers were characterized using different techniques. In vitro DOX release behavior was examined using UV-vis spectroscopy under both neutral and acidic conditions. The anticancer activity of the drug-loaded composite nanofibers was evaluated via the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) viability assay and phase contrast microscopic morphology observation of a model KB cancer cell line (a human epithelial carcinoma cell line). We show that DOX can be successfully loaded onto the surface of the n-HA and the formed composite fibers have a uniform and continuous fibrous morphology. Importantly, the loaded DOX shows a sustained release profile, and the released DOX from the nanofibers displays non-compromised antitumor activity towards the growth inhibition of KB cells. With the significantly reduced burst release profile and the improved mechanical durability of the composite nanofiber system compared with n-HA-free PLGA nanofibers, the designed organic–inorganic hybrid nanofibers could be used as a versatile drug delivery system for encapsulation and sustained release of different drugs with prolonged therapeutic efficacy for different biomedical applications.