The phase generated carrier (PGC) demodulation technique is widely used in distributed fiber-optic interferometric sensors, for its high sensitivity, good linearity, and large dynamic range. An improved PGC demodulation algorithm with single-path differential divide and the differential-self-multiplication (PGC-SDD-DSM) demodulation algorithm is proposed in this paper, the demodulation result of the PGC-SDD-DSM algorithm is not related to the carrier phase modulation depth (C) and light intensity disturbance (LID). The simulation and experiment results show that the proposed algorithm is insensitive to the C value, and compared with the single-path differential divide to PGC demodulation algorithm (PGC-SDD), the traditional differential-cross-multiplying (PGC-DCM) and PGC Arctangent (PGC-Arctan) demodulation algorithms, and the proposed algorithm has the best demodulation effect. When the proposed demodulation algorithm is applied in the optical fiber interferometric, it is found that the proposed algorithm can suppress the distortion caused by LID and C. The frequency of the signal to be demodulated is 1000 Hz, and the amplitude value is 2 rad. When the carrier modulation depth of 1.5 rad and the light intensity interference depth of 0.7 rad are introduced, the signal-to-noise and distortion ratio (SINAD) of the demodulation result using the improved PGC demodulation algorithm in the experimental system is 35.56 dB, which is 10.87 dB, 24.19 dB, and 6.38 dB higher than using traditional PGC-DCM, PGC-Arctan, and PGC-SDD demodulation algorithms, respectively. It is proved the system's stability improved effectively. This technology effectively promotes technical research in the fields of optical fiber sensors.