The corrugated steel plate has been widely used in steel and composite structures due to its large out-of-plane flexural stiffness. An innovative type of steel–concrete composite wall using corrugated steel plates called multi-celled corrugated-plate concrete-filled steel tubular (MC-CFST) wall has been proposed recently. In order to study its performance under axial compression, numerical analysis was conducted in this paper. A refined finite element (FE) model was established and validated by previous test results. The vertical and out-of-plane normal stresses of concrete and strains of corrugated steel plates were analyzed, indicating that the corrugated steel plates had a good confinement effect on the infilled concrete. Then, a parametric analysis was conducted to investigate the effect of various parameters on the axial compressive performance of MC-CFST walls. The main parameters included corrugated cell width, wall depth, thicknesses of corrugated steel plates and steel tubes, concrete and steel strengths and corrugation amplitude. Finally, the equivalent confinement factor ξw was defined to evaluate the confinement effect of corrugated steel plates on the infilled concrete. On this basis, a design formula for calculating the ultimate resistance of the MC-CFST wall was proposed. The proposed formula exhibited good agreement with experimental and numerical results, and it could provide valuable references for the design of MC-CFST walls in practice.