The Phase Generated Carrier (PGC) demodulation algorithm is currently an important demodulation algorithm in the field of fiber optic interferometric sensing. To overcome the problem of light intensity perturbation and modulation depth affecting the accuracy of signal demodulation in the current PGC demodulation algorithm, an improved PGC demodulation algorithm (PGC-Ameliorated) is proposed, and a vibration sensing system based on Distributed Feedback (DFB) lasers is built for experimental verification. The experimental results show that when the frequency of the measured vibration signal is 800Hz, the signal-to-noise ratio of the algorithm is 57dB; this is better than those of the Differential and Cross Multiplying (DCM) and Arctan algorithms. At different values of light intensity, the amplitude of the demodulated signal fluctuates in the range of ±0.02rad. At different values of modulation depth, the algorithm exhibits a minimum total harmonic distortion of 0.61% and a maximum signal-to-noise ratio of 25.9dB that provides lower total harmonic distortion and higher signal-to-noise ratio than the DCM and Arctan algorithms.