The interferometric fiber optic hydrophone based on a 3×3 coupler has reached the stage of engineering application in marine target monitoring. Typically, the phase shift signal demodulation employs ellipse fitting based on the least squares method to estimate the parameters of the interference signal, thereby addressing the demodulation bias caused by non-ideal 3×3 couplers. However, when the fiber optic hydrophone receives weak signals and the phase shift generated by the interferometer is small, the Lissajous ellipse formed by the interference signal becomes incomplete. In such cases, the high curvature bias issue of the least squares method leads to significant deviations in the demodulated phase shift signal. Additionally, although the orthogonal distance fitting method can effectively fit incomplete ellipses, its computational complexity and time-consuming nature are unsuitable for real-time demodulation. To address these challenges, this article proposes a weak signal demodulation method for fiber optic hydrophones based on Sampson distance parameter estimation. By utilizing Sampson distance to fit the incomplete Lissajous ellipse formed when the 3×3 coupler fiber optic hydrophone receives weak signals, the parameters of the output interference signal can be accurately estimated. This approach not only improves demodulation accuracy but also significantly enhances computational efficiency, outperforming the orthogonal distance fitting method. Through numerical simulations, the demodulation results of Sampson distance, the least squares method, and the orthogonal distance are compared and analyzed. The results show that the proposed Sampson distance demodulation method exhibits smaller fitting and demodulation errors under weak signal conditions compared to the least squares method and requires significantly less computation time than the orthogonal distance method. Experimental comparisons of the fiber optic hydrophone demodulation method are implemented within the frequency ranges of 10 to 30 kHz and 20 Hz to 2 kHz using a laser interferometry free-field calibration system and a vibrating liquid column low-frequency calibration system, respectively. The effectiveness of the proposed Sampson distance demodulation method is validated.