This study specifically focuses on the damping efficiency of a damped structure with additional viscous dampers. A two-layer steel frame structure with eight sets of viscous dampers is used to conduct a series of seismic simulation shaking table tests, including a non-damped structure without dampers and two damped structures with dampers placed at 1/2 and 1/6 of the beam span, respectively. By conducting these tests, the energy dissipation, force, and displacement of the damper, as well as the parameters of the structure such as floor displacement and acceleration, are obtained. The main damping efficiency indicators of the damped structure are calculated, including the additional damping ratio, inter-story displacement utilization rate, as well as the reduction rate of the vertex displacement and the base shear relative to the non-damped structure. The study shows that the viscous dampers exhibit full hysteresis loops and a strong energy dissipation capacity in the structure. The seismic response of the vertex displacement and base shear in the damped structure is significantly smaller than that in the non-damped structure. Under different seismic levels, including frequent earthquakes, occasional earthquakes, and rare earthquakes, the damping effect of the dampers placed at 1/2 of the beam span is significantly better than that placed at 1/6 of the beam span. For example, the additional damping ratio for the X-direction artificial wave REN is 19% and 11%, 20% and 13%, and 13% and 11%, respectively. The patterns for inter-story displacement utilization ratio, reduction rate of the vertex displacement, and reduction rate of the base shear are similar. The research findings strongly indicate that the damped structure with additional viscous dampers exhibits excellent damping efficiency. In future damping design, designers need to fully consider the placement of viscous dampers within the beam span.