This paper presents a novel steel-damping-concrete (SDC) composite wall as a vertical element for high-rise buildings and nuclear power plants etc. In an SDC composite wall, a damping layer is sandwiched between the concrete core and steel plates to reduce structural response based on its damping characteristics under axial and seismic loads. To ensure that an SDC composite wall exhibits a comparable compressive resistance as a steel-concrete-steel (SCS) composite wall, two types of reinforcing approaches including steel sheets and sleeves are utilized to enhance the weakness of the damping layer on the concrete core. The compressive performance of the reinforced SDC composite wall is numerically and analytically investigated using finite element (FE) simulations by ABAQUS. The influences of several key parameters including the type of reinforcement, the thickness of the damping layer, steel plates, and concrete core, the binding bar spacing as well as the diameter of steel sheets on the compressive performance of the composite walls are investigated through numerical analyses. The results show that while only embedding the rubber interlayer in the composite wall leads to the decrease of compressive resistance of the composite wall, the steel sheets and sleeves can provide the confinement effect on concrete core efficiently and improve the compressive resistance and ductility of walls. Based on the available methods in the current design codes such as Eurocode 4, AISC-360, a theoretical model is developed to predict the ultimate compressive resistance of SDC walls. The predictions show a reasonable correlation when compared with the numerical results.