A novel cambered surface steel tube damper (CSTD) with a cambered surface steel tube and two concave connecting plates is proposed herein. The steel tube is the main energy dissipation component and comprises a weakened segment in the middle, a transition segment, and an embedded segment. It is believed that during an earthquake, the middle weakened segment of the CSTD will be damaged, whereas the reliability of the end connection is ensured. Theoretical and experimental studies are conducted to verify the effectiveness of the proposed CSTD. Formulas for the initial stiffness and yield force of the CSTD are proposed. Subsequently, two CSTD specimens with different steel tube thicknesses are fabricated and tested under cyclic quasi-static loads. The result shows that the CSTD yields a stable hysteretic response and affords excellent energy dissipation. A parametric study is conducted to investigate the effects of the steel tube height, diameter, and thickness on the seismic performance of the CSTD. Compared with equal-stiffness design steel tube dampers, the CSTD exhibits better energy dissipation performance, more stable hysteretic response, and better uniformity in plastic deformation distributions.