To improve the recoverability of structures following an earthquake, a Reid friction damper with self-centering characteristics is proposed and its hysteretic behavior is studied by theoretical analysis and experimental research. The main parameters of the damper are the equivalent stiffness and energy dissipation coefficient. Based on a 10-story steel frame structure, 10 energy dissipation design schemes using the proposed Reid damper are proposed. The additional equivalent damping ratios of the 10 schemes are equal, whereas the energy dissipation coefficients of the dampers are different. The vibration control effects of the energy dissipation structures are analytically investigated under four earthquake loads. The experimental results of the friction damper are in good agreement with the theoretical results, and the hysteretic behavior of the damper follows that of a typical Reid model. The seismic response and structural damage can be reduced using any of the 10 design schemes; however, the effects are different. When the energy dissipation coefficient is in the range of 0.1–0.3, the control effect on the interstory drift is better; however, the structural acceleration response and damping force of the dampers increase. When the energy dissipation coefficient is in the range of 0.6–1.0, the energy dissipation effect of the dampers is good; however, the self-centering ability is poor. Therefore, the optimum range of the energy dissipation coefficient of a Reid damper intended for energy dissipation structures should be 0.3–0.6.