Environment temperature changes and vibration will cause the random change of phase difference between two arms in the MachZehnder interferometer (MZI), resulting in the instability of interferometer outputs. In this paper, the effect of temperature and vibration on the 3×3 couplerbased interferometer was studied in detail under natural conditions. Results show that the interference frequency caused by temperature and vibration is mainly concentrated in the low frequency section below 100 Hz. In order to eliminate these disturbances, a singlearm compensation feedback loop was designed to stabilize the output signal, and a dynamic compensation method was proposed based on quadrant judgment for distinguishment of positive and negative feedback. In the experiments, two of the three outputs of the 3×3 coupler are transformed from optical single to electrical one, and drives the piezoelectric ceramic to stretch the fiber wound on it after differential amplifier and other feedback circuits, which dynamicly compensate the phase difference drift of the interferometer and stablize the output namely the third output of the 3×3 coupler. Considering the disturbances caused by the temperature and vibration under nature environment, a stable dynamic compensation device was successfully demonstrated which can effectively suppress lowfrequency interference below 160 Hz, and compensate realtime the phase difference drift between two arms of the interferometer, while the output becomes stable with fluctuations less than 5.64%.