Laser linewidth measurement based on the delayed self-heterodyne interferometer using a Mach-Zehnder modulator (MZM) is proposed and demonstrated. Instead of the single-sideband modulation in an acousto-optic modulator (AOM), the proposed scheme is implemented using carrier-suppressed double sideband modulation in the MZM. The experiment agrees well with the theoretical derivation. Data analysis by Voigt curve fitting shows that the proposed approach based on the MZM can get the similar full width at half maximum (FWHM) as the conventional approach using an AOM.