In this paper, a method to obtain the quantum capacitance of carbon nanotubes (CNTs) using ab initio simulations is presented. As an example of the usage of the proposed method, the quantum capacitance of a metallic (6,6) CNT section is calculated. The quantum capacitance is extracted for various bias voltages applied to metallic CNT interconnects in the range 0-2.5V, which is the operating voltage range of VLSI circuits. The obtained quantum capacitance values are found to be in good agreement with the experimental values. The average Fermi velocity of electrons dependent on the bias voltage is also obtained and plotted.