Electrospun composite scaffolds show high ability to be used in regenerative medicine and drug delivery, due to the nanofibrous structure and high surface area to volume ratio. In this study, we used nanofibrous scaffolds fabricated by chitosan (CS), poly(vinyl alcohol) (PVA), carbopol, and polycaprolactone using a dual electrospinning technique while curcumin (Cur) incorporated inside of the CS/PVA fibers. Scaffolds were fully characterized via scanning electron microscopy, water contact angle, tensile measurement, hydration, protein adsorption, and wrinkled tests. Furthermore, viability of the buccal fat pad‐derived mesenchymal stem cells (BFP‐MSCs) was also investigated using MTT assay for up to 14 days while cultured on these scaffolds. Cell cycle assay was also performed to more detailed evaluation of the stem cells growth when grown on scaffolds (with and without Cur) compared with the culture plate. Results demonstrated that Cur loaded nanofibrous scaffold had more suitable capability for water absorption and mechanical properties compared with the scaffold without Cur and it could also support the stem cells viability and proliferation. Cur release profile showed a decreasing effect on BFP‐MSCs viability in the initial stage, but it showed a positive effect on stem cell viability in a long‐term manner. In general, the results indicated that this nanofibrous scaffold has great potential as a delivery of the Cur and BFP‐MSCs simultaneously, and so holds the promising potential for use in various regenerative medicine applications.