Nowadays, vibration energy absorption devices are widely implemented in many buildings subjected to severe vibration due to natural hazards, such as earthquakes, strong winds, and typhoons. Recently, viscous dampers have been commonly used in many structures as the most conventional damper type. However, the high maintenance cost resulting from oil leakage from cylinder seals has prompted researchers to seek an alternative system to viscous damper systems. Therefore, the main aim of this research is to develop a new rubber bracing damper (RBD) system by implementing high damping rubber material as a viscoelastic material to be installed in framed structures as diagonal bracing members. This will help dissipate vibration effects on the structure. To achieve this, the initial design for the RBD device has been developed, and finite-element simulation has been conducted to evaluate the behavior of the proposed RBD under various dynamic loading conditions. To define the viscoelastic material properties in finite-element modeling, high damping rubber material has been produced and experimentally tested to determine the numerical model of the material. Subsequently, the test data were utilized to develop the analytical model of the RBD device, and its performance was evaluated by applying cyclic loads and conducting nonlinear analysis. Furthermore, a series of cyclic dynamic tests with various displacement amplitudes and frequencies have been conducted on the prototype of the RBD device based on the finite-element results. Finally, to analyze the dynamic behavior of the structure equipped with RBD, a finite-element model of a three-story reinforced concrete frame structure furnished with RBD dampers has been developed. The response of the structure has been evaluated under seismic loads, and a parametric study has been conducted to investigate the response of the structures with various rubber properties. The numerical analysis results indicated that the implementation of the RBD device leads to a reduction in the occurrence of plastic hinges and lateral displacements of the structure by up to 69%. This demonstrates the efficiency of the RBD device in diminishing the seismic load effect on the structure’s response.