We characterized the dynamic response of a Bragg grating-based fiber laser sensing system. The sensing system comprises of a narrow line width fiber laser based on -phase-shifted fiber Bragg grating formed in an active fiber, an unbalanced fiber Michelson interferometer (FMI), which performs wavelength-to-phase mapping, and a phase detection algorithm, which acquires the phase change from the interferometric output signal. The novel phase detection algorithm is developed based on the combination of the two traditional phase generated carrier algorithms: differential-cross-multiplying and arctangent algorithms, and possesses the advantages of the two algorithms. The modulation depth fluctuation of the carrier does not affect the performance of the sensing system. A relatively high side mode suppression ratio of above 50 dB has been achieved within a wide range of carrier amplitude from 1.6 to 5.0 V which correspond to the modulation depth from 1.314 to 4.106 rad. The linearity is 99.082% for the relationship between the power spectral density () of the detected signal and the amplitude (mv) of the test signal. The unbalanced FMI is used to eliminate the polarization effect.