Mesenchymal stem cells (MSCs) have attracted considerable attention in cell therapies and tissue engineering for their multilineage differentiation potential and immunomodulatory properties. However, MSCs gradually lose their stemness and multipotentiality in prolonged two-dimensional (2D) culture in vitro. Herein, a three-dimensional (3D) polyethylene terephthalate (PET) microfiber sponge served as the substrate, and gelatin macromolecules were grafted onto PET through the adsorption of polydopamine to prepare a 3D cell carrier (PET-Gel) with an interpenetrating network structure. The cell carrier could be sterilized by autoclaving. The material characterization results showed that the 3D carrier had good coating stability, thermal stability, and mechanical properties; these properties did not decrease after autoclaving. In vitro cell experiments revealed that the 3D cell carrier promoted the adhesion and proliferation of human umbilical cord MSCs (HUCMSCs). In long-term culture (2 weeks), the cell proliferation rate was 2.4-fold higher than that on 2D plates because the interpenetrating network structure of the carrier led to a larger growing area than 2D plates and the cells infiltrated into the interior of the carrier. Simultaneously, HUCMSCs on PET-Gel expressed surface-specific antigens of the MSCs. The typical paracrine cytokine expression was characterized using qPCR and Western blotting. The paracrine function of cells on the 3D carrier was nearly equivalent to that on the 2D plates. These results showed that the PET-Gel carrier was suitable for the long-term culture of HUCMSCs in vitro.