Cancer is one of the most fatal diseases in the world. Chemotherapy and radiation therapy are conventional cancer treatments affecting healthy tissues and also have many side effects. Drug delivery systems based on nanofibers can be used as cancer drug carrier with the least side effects. 5FU is one of the most common medicines for many types of cancer. In this study, PCL/PVP core-shell nanofibers containing MWCNTs were performed as 5FU carrier, which was loaded in core of these nanofibers. FESEM images showed all these core-shell nanofibers are uniform and the average diameter was 300-400 nm. There was no interaction between components of nanofibers, and the presence of 5FU in nanofibers was confirmed. The presence of MWCNTs loaded in shell improved the tensile properties. The degradability of nanofibers was investigated, and it was improved by increasing PVP in nanofibers. The morphology change in nanofibers was investigated by FESEM images after degradation. The release behavior of nanofibers was studied. These nanofibers had sustained and prolonged release, and the optimum sample in which 85% of drug released after 528 h was used for cytotoxicity test. The drug release mechanism was modeled by various mathematical models and followed Fick's law. MTT assay on HeLa cell line showed that cell cytotoxicity of 5FU loaded nanofibers was 50.35% after 72 h. The non-toxicity of carrier and efficacy of the drug loaded nanofibers mat on cervical cancer cell line were confirmed. This drug delivery system has the potential to perform as post-surgical anticancer drug delivery system.