We report a higher precision measurement of the refractive index of carbon dioxide using a frequency comb as the light source in a Mach-Zehnder interferometer setup. The experimental sensitivity can reach the level of 8.8x10(-9). Taking into account the measurement accuracy of temperature and pressure, the experimental accuracy has a value of 1.2x10(-8). The measurement result has a deviation from the commonly quoted result [Old , J. Opt. Soc. Am.61, 89 (1971)] by 6.4x10(-7) at 800 nm.