The emission of light wave from a pulsed broadband source controlled by a clock is injected into a four-element fiber Bragg grating sensor array. A technique of time-domain addressing is introduced to interrogate the gratings spaced 10 m apart by employing a 1×4 analog electrical switches, which is controlled by the same clock. The switches allocate the pulses reflected by the sensor elements into corresponding output channels to make the system performing the function of real-time monitoring the measurand. Demodulated with an unbalanced Michelson interferometer, which converts the wavelength shifts to phase changes, the system is demonstrated to be with a sensing sensitivity of 1.658°/με at the wavelength of 1556 nm. It matches the theoretical value of 1.673°/με basically.