The intensity noise caused by the relaxation oscillation in lasers has a great influence on the system noise in the distributed feedback fiber laser hydrophone. The transmission process of the intensity noise in the digital realization of the NPS (Naval Postgraduate School) algorithm is analyzed, and it is found that the non-ideal characteristic of the derivation operation is the reason for the introduction of intensity noises in the demodulation results. An improved symmetric demodulation algorithm is proposed, where the intensity noise is canceled before entering the derivation operation and the way of the intensity noise transferring to the demodulation results is eliminated. The experimental results show that the demodulated phase noise suppression at 1 kHz reaches 30 dB when the relative intensity noise at the relaxation oscillation peak is -84 dB·Hz-1. The improved algorithm is compared with the arctangent method where the derivative operation is not needed and is further verified to suppress the intensity noise introduced by the derivation.