Biogas is an interesting fuel for hydrogen production in solid oxide fuel cell (SOFC). However, CO2 is a main composition of biogas, resulting in the dilution of hydrogen in syngas and low electrical efficiency of SOFC. To increase the hydrogen concentration, the power plant of biogas-fuelled SOFC requires the installation of carbon dioxide-selective membrane separator. The aim of this work is the performance analysis of the power plant of SOFC system utilizing biogas as fuel with and without installing the CO2-selective membrane separator. The simulation results showed that the membrane area has direct effect on the amount of permeated CO2 and the system performance. The increase of membrane area of separator enhances the SOFC and thermal efficiencies. However, the hydrogen loss in the retentate side increases and resulting in the decrement of system electrical efficiency. When considering performance of both systems, the SOFC efficiency of the SOFC system with CO2-selective membrane separator is superior to the conventional system about 7.54%. Also, its thermal efficiency is higher, compared to the conventional system.