Viscoelastic (VE) dampers have shown to be capable of providing structures with considerable additional damping to reduce the dynamic response of structures. However, the VE material appears to be sensitive to the variations in ambient temperature and vibration frequency. To minimize these effects, a new VE material has been developed. This new material shows less sensitivity to variations in vibration frequency and temperature. However, it is highly dependent on the shear strain. Experimental studies on the seismic behavior of a 2/5 scale five-story steel frame with these new VE dampers have been carried out. Test results show that the structural response can be effectively reduced due to the added stiffness and damping provided by the new type of VE dampers under both mild and strong earthquake ground motions. In addition, analytical studies have been carried out to describe the strain-dependent behavior of the VE damper. The dynamic properties and hysteresis behavior of the dampers can be simulated by a simple bilinear model based on the equivalent dissipated energy principle proposed in this study.