As a noncontact high-precision optical full-field measurement method, shearography can be used for the nondestructive detection of internal defects in composite materials. However, the obtained phase fringe pattern contains a high amount of speckle noise that seriously affects the detection results and accuracy. Therefore, we propose a phase fringe-filtering method using an unsupervised image style conversion model (CycleGAN). Furthermore, the original noise phase fringe image obtained using shearography is converted into an ideal noiseless fringe image via network training to achieve noise filtering in the phase fringe pattern. The experimental results show that the proposed method achieves high-efficiency filtering for noise in areas where the stripe distribution is relatively sparse, with clear boundaries and significant contrast in filtered images. Additionally, the running time of the proposed method is better than that of the other methods (by approximately 30 ms), achieves high-quality filtering, meets the development demand of dynamic nondestructive testing, and provides a new idea for the noise filtering of phase fringe pattern.