To improve the damping performance of a shape memory alloy (SMA), we propose a concept of active tuning of its pseudoelastic property where the shape of the stress–strain curve is modified as desired by utilizing the material's strong thermo-mechanical coupling characteristic. Simulated results are presented for a structural system in which SMA wires are used to suppress the vibration of a cantilevered beam by controlling the wire temperature using an electric current. This control increases the area of inherent hysteresis loop associated with the pseudoelastic effect and a large damping is obtained. In the system discussed, airflow is applied for cooling. It is shown that under forced heat convection the wire temperature can be changed fast enough to control a structure vibrating at more than 5 Hz. Simulated results seem to promise that the active tuning of SMA characteristics can increase its already high inherent damping by a factor of more than two. Experiments are also performed to validate the SMA model used in the numerical simulations.