The paper focuses on investigating a novel sandwich panel, which incorporates extruded polystyrene foam boards placed between the inner and outer concrete panels. These are connected using various types of shear connectors to achieve a composite action, meeting the bending resistance requirements. To study the structural performance of the sandwich panels, three representative specimens were designed. These specimens employed different types of shear connectors, namely, steel truss connectors with inclined bars at 45°, and GFRP connectors with inclined bars at 45° and 30°, respectively. The specimens underwent full-scale testing using a step-by-step four-point loading method. The test results indicated shear-compression failure of the specimens, exhibiting consistent failure modes across all specimens, and a composite action in resisting bending moments. Based on theoretical stress–strain diagrams and considering the slip phenomenon between the concrete panel and the connectors, this paper establishes an analytical model. It can reasonably estimate the ultimate load-carrying capacity of sandwich insulation panels under shear-compression failure, which has implications for subsequent engineering applications.