The random disturbance in the leading fiber is considered as a vital noise source in the practical interferometric fiber Bragg grating (FBG) sensor array, which is usually interrogated by periodic laser pulse pair. As the two interrogation laser pluses propagate through the leading fiber in a time-sharing manner, the leading fiber disturbance could cause undesired demodulated phase noises to both the polarization state and the pulse-interval, which are summarized as the polarization fading induced noise and the Doppler noise, respectively. This paper focused on the Doppler noise under the demodulation scheme of polarization switching (PS) and phase generated carrier (PGC) hybrid processing method. A model describing the transformation from arbitrary leading fiber stretching to sensor phase background was presented. The complexity was that the Doppler noise was coupled with the birefringence states, as verified by both simulation and experiment. In response to this issue, a two-stage Doppler noise suppression method was proposed, which is based on the PS and PGC hybrid processing and a reference sensor. A processing procedure was presented where the polarization synthesis must be performed before and the reference sensor was considered. Otherwise, the suppression algorithm will be completely invalid due to the mutual coupling of the Doppler noise and the birefringence. Experimental results showed that only after the first stage of polarization synthesis, identical Doppler noise in the two TDM channels could be obtained, with an amplitude error of 0.02 dB. The second stage involved non-sensitive reference sensor subtraction, which achieved a maximum suppression of about 30 dB, which was the highest to be best of our knowledge. The two-stage Doppler noise suppression method was tested for sinusoidal and wideband leading fiber disturbances, providing a solution for practical interferometric FBG array applications.