This study investigates the experimental response of a hybrid damper that combines superelastic shape memory alloy (SMA) cables with a high damped butyl rubber compound. A prototype device with a load capacity of 40 kN and stroke capacity of 100 mm is designed and fabricated. First, two butyl rubber elastomer compounds are sandwiched and bonded to three steel plates. Then, delrin rods are attached to the steel plates to provide a smooth contact and low friction between the steel plates and SMA cable. Next, SMA cables are wrapped around the top and bottom steel plates to complete the damper. The developed damper is subjected to cyclic loading at increasing displacement amplitudes up to 100 mm. The tests are conducted at various loading frequencies ranging from 0.1 Hz to 2.0 Hz to reveal any rate-dependent behavior of the damper. High-speed video cameras are used to monitor the full-field strains and displacement in the SMA cable and elastomer compounds. Furthermore, an infrared thermal camera is used to monitor the full temperature profile change in the viscoelastic and SMA cable. Test results are analyzed to assess the energy dissipation and re-centering capabilities of the developed damper. In addition, a high fidelity finite element model of the damper is developed and validated using the experimental results. The developed model is used to conduct further parametric studies on the effects of SMA and butyl rubber parameters such as length, cross-sectional area, and thickness on the damper performance.