Concrete-Filled Double Skin Tubular (CFDST) beams with stainless steel as the outer tube, carbon steel as the inner tube and sandwiched concrete infill between the tubes are presented. Previous studies on CFDST beams have revealed significant enhancements in flexural capacity due to the interaction between concrete and metal tubes. In this study, an innovative form of CFDST beam has been proposed, whereby the inner tube is positioned in the tensile zone of the sections. Hence, the beam sections can resist higher bending moment compared to those sections with the inner tube located at the centroid. A series of tests was performed on CFDST beams with an eccentric inner tube. Nine three-point major-axis bending tests were conducted. The full moment–deflection histories, moment capacities and failure modes of the CFDST beams are presented herein. The experimental results were used to evaluate the bending resistances predicted by the American and European Specifications.