Abstract: We introduce the technique of narrow-linewidth optical frequency combs. A method based on the Mach-Zehnder Interferometer with electro-optic modulators was demonstrated to be able to fast control the carrier-envelope offset frequency. A relevant theoretical analysis and simulation were carried out. An experimental frequency comb based on the Mach-Zehnder Interferometer with electro-optic modulators was built in our lab. An ultra-stable laser with the linewidth of about 1 Hz was employed to beat with the comb to verify the capability of the Mach-Zehnder Interferometer. A carrier-envelope offset frequency shift of about 8.2 MHz was achieved. This method provides a technical solution for narrow-linewidth optical frequency combs.