A CFPBS (Cone-type Friction Pendulum Bearing System) was developed to control the acceleration delivered to a structure to prevent the damage and degradation of critical communication equipment during earthquakes. This study evaluated the isolation performance of the CFPBS by numerical analysis. The CFPBS was manufactured in the shape of a cone differenced with the existing FPS (Friction Pendulum System), and a pattern was engraved on the friction surface. The natural frequencies of the CFPBS were evaluated from a free-vibration test with a seismic isolator system consisting of 4 CFPBS. To confirm the earthquake-resistant performance, a numerical analysis program was prepared using the equation of the CFPBS induced from the equations of motion. The equation reported by Tsai for the rolling-type seismic isolation bearings was proposed to design the equation of the CFPBS. Artificial seismic waves that satisfy the maximum earthquake scale of the Korean Building Code-Structural (KBC-2005) were created and verified to review the earthquake-resistant performance of the CFPBS by numerical analysis. The superstructural mass of the CFPBS and the skew angle of friction surface were considered for numerical analysis with El Centro NS, Kobe NS and artificial seismic waves. The CFPBS isolation performance evaluation was based on the numerical analysis results, and comparative analysis was performed between the results from numerical analysis and simplified theoretical equation under the same conditions. The validity of numerical analysis was verified from the shaking table test.