Mesenchymal stem cell (MSC) transplantation, in particular allogeneic transplantation, is a promising therapy for a variety of diseases. However, before performing allograft treatment it is necessary to find suitable donors, establish culture methods that maintain cell quality, and reduce cell production costs. Here, we present a new method of producing allogeneic MSCs combining human umbilical cord-derived mesenchymal stem cells (UCMSCs) and chitin-based polysaccharide fibers (Cellhesion® MS). UCMSC numbers significantly increased, and cells grew as dispersed spheres on Cellhesion® MS. Subsequent biological analyses showed that the expression levels of stemness-related and migration-related genes were significantly upregulated, including octamer-binding transcription factor 4 (OCT4), Nanog homeobox (NANOG), and C-X-C chemokine receptor type 4 (CXCR4). The secretion levels of paracrine factors such as prostaglandin E2 (PGE2), TNFα-stimulating gene (TSG)-6, fibroblast growth factor 2 (bFGF), and Angiogenin (Ang) from UCMSCs using Cellhesion® MS were significantly higher than with microcarrier and U-bottom plate culture. In addition, culture supernatant from UCMSCs with Cellhesion® MS had better angiogenic potential than that from monolayer cultured UCMSCs. Furthermore, we succeeded in a scaled-up culture of UCMSCs with Cellhesion® MS using a closed culture bag. Therefore, Cellhesion® MS is a key material for producing high-quality UCMSCs in a three-dimensional (3D) culture system.