To address the issue of harsh marine background noise impacting the monitoring signal of fiber-optic hydrophones, we propose a low-noise fiber Bragg grating (FBG) hydroacoustic monitoring system with a reference sensor based on genetic algorithm backpropagation (GA-BP). Through theoretical analysis, we deduce the noise suppression steps of the GA-BP algorithm based on the reference sensor and construct train and test sets based on the data from the reference sensor and monitoring sensor at different times, optimizing the GA-BP algorithm to find the best fitting results and thereby obtaining the low-noise monitoring signal. Experimental results from the anechoic tank show that the proposed method can suppress background noise interference on effective signals and that the suppression effect improves as the background noise increases. The sound pressure sensitivity ranges from -173.76 dB to -171.33 dB at frequencies of 8 kHz to 12 kHz, with a response flatness of less than 2.43 dB. The noise suppression effect is obvious under the condition of poor signal-to-noise ratio (SNR), which can reach more than 18.3 dB. The advantages of the proposed algorithm in array signal processing are further demonstrated by the directivity experiment, which proves that the algorithm has a great potential for engineering applications in harsh marine environment.