A simple method for a time delay measurement of a chirped fiber grating by using bidirectional modulation of a Mach-Zehnder modulator has been proposed. The bidirectionally modulated light with time difference makes an interference fringe in the RF domain. The time delay of a chirped fiber grating can be obtained by measuring the period of the RF interference fringe for different wavelengths. We have measured the time delay of a chirped fiber grating with a chirped length of 5 cm and a bandwidth of 3.16 nm. The average slope of the time delay has been measured to be 183 ps/nm and its uncertainty has been less than $pm$1.7%.