A magnetorheological fluid(MR fluid) is a type of smart fluid in a carrier fluid, usually a type of oil. When subjected to a magnetic field, the fluid greatly increases its apparent viscosity, to the point of becoming a viscoelastic solid. And, Shape-memory polyurethane(SMPU) is a kind of polymeric smart materials that have the ability to return from a deformed state to their original shape induced by an external stimulus, such as temperature change. In this study, the multi-functional fiber webs showing magnetorheological(MR) property under magnetic field and shape memory(SM) effect by heat were prepared by coaxial electrospinning process. The fibers were designed to consist of two part; core part, SMPU+MRF and sheath part, SMPU. Consequently, we found that ca. 10 wt% MRF+15 wt% SMPU solution is most suitable for core part dope solution, and 17 wt% SMPU solution is most suitable for sheath part dope solution. Through scanning electron microscope(SEM) and transmission electron microscope(TEM), we observed stable core/sheath structure in the fiber of the electrospun web. From the dynamic mechanical analyzer(DMA) result to investigate the shape recovery ability of the fibe webs by heat, we discovered reasonable shape recovery property from the electrospun fiber web. Also, they showed MR effect under magnetic field through universal testing machine(UTM) test.