In this study, the axial compressive performance of steel–concrete–steel composite walls (SCSCWs) with novel dumbbell-shaped connectors (DSCs) was investigated. Six specimens were designed and tested, and the study parameters included the physical dimensions and arrangement schemes of DSCs. The failure mode, axial displacement, steel strain, and bearing capacity of the specimens were analyzed. The external steel plates exhibited local buckling, and the internal concrete was crushed. The variation in the physical dimensions of the DSC had little effect on the failure modes, and increasing the number of connectors improved the bearing capacity of the specimens. The axial load–displacement relationships of the SCSCWs were calculated considering the effects of local buckling and post-buckling behavior of steel faceplates in the constitutive relationship. The theoretical curves were in good agreement with the experimental results. A simplified formula for the bearing capacity was proposed, and the average ratio of the experimental to theoretical peak loads was 0.98, indicating that the simplified formula had high accuracy. ABAQUS software was used to simulate the axial behavior of SCSCWs. The simulated results were similar to those of the experiments, and the average ratio of the experimental bearing capacity to the corresponding simulated value was 0.99. Based on the benchmark model, further parameter analyses were conducted to study the effects of material strength and physical dimensions on the axial behavior of SCSCWs. Increasing the material strength and sectional thickness could increase the bearing capacity, and the failure mode was not affected. The theoretical initial stiffness of the SCSCWs was calculated, and the accuracy of the formulas was verified using the simulated results.