Conventional electrospun nanofibrous membranes have been widely used for tissue engineering scaffolds because they can mimic extracellular matrix (ECM), which plays a significant role in cell proliferation, adhesion, and differentiation. However, the inadequate mechanical strength and biological functions of electrospun nanofibrous scaffolds limit the range of their practical applications. In this study, we prepared a uniform levan-based core-shell composite (csCAL) nanofibrous membrane using the coaxial electrospinning technique. The coaxial csCAL membrane with levan and cellulose acetate (CA) as shell and core, respectively, exhibited highly enhanced mechanical properties and adhesive strength. Moreover, the unique bioadhesive nature of these membranes significantly enhanced cell attachment and proliferation, while their high biocompatibility and biodegradability hold substantial promise for application as functional cell carriers. Upon incorporating mesenchymal stem cells (MSCs) into the csCAL nanofibrous membrane, we observed enhanced osteogenesis and chondrogenesis, as evidenced by alizarin red and alcian blue staining, respectively. These results indicate that the levan-based nanofiber architecture has the potential to deliver scaffolds for supporting the differentiation of MSCs.