A variety of surface modification techniques have been proposed to improve the cell-biomaterial interactions. On the other hand, these processes may cleave long-chained polymers, and compromise their mechanical properties. In this study, dopamine was used as a bridge molecule to immobilize gelatin on the poly(L-lactide-co-${varepsilon}$-caprolactone) (PLCL) fibrous matrices, which may then be used as a cell delivery carrier. The PLCL fibrous matrices coated with polydopamine by dipping (D-PLCL) can subsequently immobilize gelatin (GD-PLCL). The D-PLCL matrices showed minimal changes in the mechanical properties with a tensile strain of $251.0{pm}33.4%$ and $247.8{pm}32.1%$ before and after the coating process, respectively. The cellular activities on the fibrous matrices increased in the order of PLCL<G-PLCL<D-PLCL<GD-PLCL; the H9c2 myoblasts on the GD-PLCL matrices showed approximately two-times higher adhesion and spreading than those on the PLCL matrices, and the proliferation was significantly greater on the GD-PLCL matrices than on the other matrices. Therefore, polydopamine can effectively immobilize the bioactive functional groups on the surface of electrospun fibrous matrices for the development of a tissue specific cell delivery carrier.