Friction pendulum system (FPS) has hysteresis characteristics determined by the shape of the friction surface. The shape of the friction surface of FPS is largely classified into spherical and conical. Spherical friction pendulum isolator (SFPI) occurs linear elastic behavior when there is no friction force, and conical friction pendulum isolator (CFPI) occurs nonlinear elastic behavior. Most seismic isolators are required to bear large deformations, and in this case, it is easier to design CFPI to have a smaller load applied to the device than SFPI. However, CFPI has a difficult to estimate the eigenvalue of the isolator, and it has a flagship and pinching type hysteresis curve depending on the friction coefficient and angle of the friction surface. Most CFPI designs are performed through numerical analysis, and the size of the device is determined based on the deformation predicted by the analysis. In this study, we propose the energy-based seismic design method for CFPI that can be performed without numerical analysis. Here, the formalization of CFPI is possible if the superstructure movement path on the friction surface due to the ground motion is assumed to be similar to CFPI and SFPI. Therefore, the point of this study is to perform the design of CFPI, which is difficult to calculate the eigenvalue, based on the geometric similarity with SFPI. It should be noted that this approach is possible because most of the input energy is concentrated in the seismic isolation layer, and the input energy by the design spectrum is considered to have a constant value in the design range of a general seismically isolated structure.