Quercetin is a potent natural antioxidant but has limited therapeutic applications due to its short half-life in body fluids. In order to improve the efficacy of quercetin and overcome its shortcomings, quercetin-encapsulated electrospun poly(lactic-co-glycolic acid)–poly(ε-caprolactone) nanofibrous controlled release system was developed using electrospinning technique. Fourier transform infrared spectroscopy, thermogravimetric, and X-ray diffraction analysis suggested the incorporation, thermal stability, and existence of encapsulated quercetin in semicrystalline state in the nanofibers. The release profiles of quercetin from the poly(lactide-co-glycolide)–polycaprolactone nanofibers in phosphate-buffered saline showed controlled release of quercetin up to 120 h. 3-(4,5-Dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay showed an evident inhibition effect of quercetin-encapsulated nanofibers against human hepatocellular carcinoma (HepG2), and the inhibition rate of 29%, 72%, and 80.1% were recorded for 1%, 2%, and 4% quercetin-encapsulated nanofibers, respectively. The formulated drug delivery system could be potentially used as an implantable anticancer drug in clinical applications in the future.