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A novel foam core sandwich structure was proposed to prevent skin wrinkling by inserting glass fibre-reinforced plastic stiffeners attached to the sandwich skins. A modified vacuum-assisted resin infusion method was used to manufacture the sandwich panels. To investigate the in-plane compression strengths and failure modes of the new foam core sandwich panels, experimental tests were performed on a series of specimens with different cross-sectional configurations, including thin skin, thick skin, and stiffened ones. In addition, analytical modelling was conducted, the results of which agreed well with the experimental results. Results indicate that upon the insertion of stiffeners, the failure mode of the foam core sandwich composite structures changed from skin wrinkling to compressive microbuckling or global buckling. Compared to thin-skin and thick-skin specimens, the average ultimate load and specific strength of the stiffened specimen were markedly improved. Thus, the concept of inserting glass fibre-reinforced plastic stiffeners might be desirable to prevent skin wrinkling in foam core sandwich structures for engineering applications