Based on the previous research on the Cam type Response Amplification Device with friction damper ( CRAD-FD ), the energy equation of the single-degree-of-freedom system installed with the damper is established, and the energy analytical solution of the CRAD-FD single-loop hysteresis under harmonic load is derived. Based on the standard energy design response spectrum of energy dissipation structure, the energy design method of CRAD-FD based on performance objective is proposed. Taking a 10-story RC frame structure as an example, the reliability of the method is verified under the action of fortification, rare and extremely rare earthquakes. The research shows that the energy analytical solution of CRAD-FD is correct, and the energy design method based on the performance target is reliable. The energy dissipation structure can obtain a similar or better damping control effect by directly installing large tonnage dampers through CRAD series small tonnage friction dampers, which reflects the response amplification effect of CRAD.