Local chemotherapy using polymer drug delivery systems has the potential to treat some cancers, including intraocular retinoblastoma, which is difficult to treat with systemically delivered drugs. Well-designed carriers can provide the required drug concentration at the target site over a prolonged time, reduce the overall drug dose needed, and suppress severe side effects. Herein, nanofibrous carriers of the anticancer agent topotecan (TPT) with a multilayered structure composed of a TPT-loaded inner layer of poly(vinyl alcohol) (PVA) and outer covering layers of polyurethane (PUR) are proposed. Scanning electron microscopy showed homogeneous incorporation of TPT into the PVA nanofibers. HPLC-FLD proved the good loading efficiency of TPT (≥85%) with a content of the pharmacologically active lactone TPT of more than 97%. In vitro release experiments demonstrated that the PUR cover layers effectively reduced the initial burst release of hydrophilic TPT. In a 3-round experiment with human retinoblastoma cells (Y-79), TPT showed prolonged release from the sandwich-structured nanofibers compared with that from a PVA monolayer, with significantly enhanced cytotoxic effects as a result of an increase in the PUR layer thickness. The presented PUR-PVA/TPT-PUR nanofibers appear to be promising carriers of active TPT lactone that could be useful for local cancer therapy.